Multinomial Experiments In Exercises 33 and 34, use the information below. A multinomial

Problem 1E In a binomial experiment, what does it mean to say that each trial is independent of the other trials?

Construct a probability distribution for (a) the number of hits in games with three at-bats. (b) the number of hits in games with four at-bats. (c) the number of hits in games with five at-bats.

The histograms shown below represent binomial distributions with the same number of trials n but different probabilities of success p. Match each probability with the correct graph. Explain your reasoning. \(p=0.25,p=0.50,p=0.75\) Equation Transcription: Text Transcription: p=0.25,p=0.50,p=0.75

The histograms shown below represent binomial distributions with the same probability of success p but different numbers of trials n. Match each value of n with the correct graph. Explain your reasoning. What happens as the value of n increases and p remains the same? \(n=4,n=8,n=12\) Equation Transcription: Text Transcription: n=4,n=8,n=12

Another proposed theory in genetics gives the corresponding probabilities for the four types of plants described in Exercise 33 as \(\frac{5}{16},\frac{4}{16},\frac{1}{16}\) and \(\frac{6}{16}\). Ten plants are selected. Find the probability that 5 will be tall and colorful, 2 will be tall and colorless, 2 will be short and colorful, and 1 will be short and colorless. ________________ Equation Transcription: Text Transcription: frac{5}{16},frac{4}{16},frac{1}{16} frac{6}{16}

Problem 2CSE Construct binomial probability distributions for p = 0.290 and (a) n = 3. (b) n = 4. (c) n = 5.

Identify the unusual values of x in each histogram in Exercise 4.

Identify the unusual values of x in each histogram in Exercise 3.

Problem 7E Mean, Variance, and Standard Deviation In Exercise, find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 50, p = 0.4

Problem 8E Mean, Variance, and Standard Deviation In Exercise, find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 84, p = 0.65

Problem 9E Mean, Variance, and Standard Deviation In Exercise, find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 124, p = 0.26

Problem 11E Identifying and Understanding Binomial Experiments In Exercise, determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why. Video Games A survey found that 49% of U.S. households own a dedicated game console. Eight U.S. households are randomly selected. The random variable represents the number of U.S. households that own a dedicated game console.

Problem 10E Mean, Variance, and Standard Deviation In Exercise, find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 316, p = 0.82

Problem 12E Identifying and Understanding Binomial Experiments In Exercise, determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why. Cards You draw five cards, one at a time, from a standard deck. You do not replace a card once it is drawn. The random variable represents the number of cards that are hearts.

Problem 13E Identifying and Understanding Binomial Experiments In Exercise, determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why. Lottery A state lottery randomly chooses 6 balls numbered from 1 through 40 without replacement. You choose six numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery.

Problem 15E Finding Binomial Probabilities In Exercise, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Fair and Accurate News Sixty percent of U.S. adults trust national newspapers to present the news fairly and accurately. You randomly select nine U.S. adults. Find the probability that the number of U.S. adults who trust national newspapers to present the news fairly and accurately is (a) exactly five, (b) at least six, and (c) less than four.

Problem 14E Identifying and Understanding Binomial Experiments In Exercise, determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why. Generation A survey found that 68% of adults ages 18 to 25 think that their generation is unique and distinct. Twelve adults ages 18 to 25 are randomly selected. The random variable represents the number of adults ages 18 to 25 who think that their generation is unique and distinct.

Problem 16E Finding Binomial Probabilities In Exercise, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Childhood Obesity Thirty-nine percent of U.S. adults think that the government should help fight childhood obesity. You randomly select six U.S. adults. Find the probability that the number of U.S. adults who think that the government should help fight childhood obesity is (a) exactly two, (b) at least four, and (c) less than three.

Problem 18E Finding Binomial Probabilities In Exercise, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Junk Food Sixty-three percent of U.S. adults oppose special taxes on junk food and soda. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who oppose special taxes on junk food and soda is (a) exactly six, (b) at least five, and (c) less than eight.

Problem 19E Finding Binomial Probabilities In Exercise, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Clothes Shopping Fifty-six percent of men do not look forward to going clothes shopping for themselves. You randomly select eight men. Find the probability that the number of men who do not look forward to going clothes shopping for themselves is (a) exactly five, (b) more than five, and (c) at most five.

Problem 17E Finding Binomial Probabilities In Exercise, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Ease of Voting Twenty-seven percent of likely U.S. voters think that it is too easy to vote in the United States. You randomly select 12 likely U.S. voters. Find the probability that the number of likely U.S. voters who think that it is too easy to vote in the United States is (a) exactly three, (b) at least four, and (c) less than eight.

Problem 22E Finding Binomial Probabilities In Exercise, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Environmentally Friendly Products Forty-three percent of adults would pay more for environmentally friendly products. You randomly select 12 adults. Find the probability that the number of adults who would pay more for environmentally friendly products is (a) exactly four, (b) more than four, and (c) between four and eight, inclusive.

Problem 23E Constructing and Graphing Binomial Distributions In Exercise, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning. 100th Birthday Sixty-seven percent of adults ages 55 and older want to reach their 100th birthday. You randomly select seven adults ages 55 and older and ask them whether they want to reach their 100th birthday. The random variable represents the number of adults ages 55 and older who want to reach their 100th birthday.

Problem 24E Constructing and Graphing Binomial Distributions In Exercise, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning. Messy Desk Thirty-eight percent of hiring managers have a negative view of workers with a messy desk. You randomly select 10 hiring managers and ask them whether they have a negative view of workers with a messy desk. The random variable represents the number of hiring managers who have a negative view of workers with a messy desk.

Problem 28E Finding and Interpreting Mean, Variance, and Standard Deviation In Exercise, find the (a) mean, (b) variance and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results. Potentially Offensive Songs Sixty-nine percent of adults think that musicians should be allowed to sing potentially offensive songs. You randomly select four adults and ask them whether they think musicians should be allowed to sing potentially offensive songs. The random variable represents the number of adults who think musicians should be allowed to sing potentially offensive songs.

Problem 26E Constructing and Graphing Binomial Distributions In Exercise, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning. School Standards Thirty-four percent of voters think that Congress should help write standards for school food. You randomly select six voters and ask them whether Congress should help write standards for school food. The random variable represents the number of voters who think that Congress should help write standards for school food.

Problem 25E Constructing and Graphing Binomial Distributions In Exercise, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning. Work Performance Forty-six percent of working mothers say that their work performance is the same as it was before giving birth. You randomly select eight working mothers and ask them how their work performance has changed since giving birth. The random variable represents the number of working mothers who say that their work performance is the same as it was before giving birth.

Problem 20E Finding Binomial Probabilities In Exercise, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Safety Recall Sixty-eight percent of adults would still consider a car brand despite product/safety recalls. You randomly select 20 adults. Find the probability that the number of adults who would still consider a car brand despite product/safety recalls is (a) exactly one, (b) more than one, and (c) at most one.

Problem 27E Finding and Interpreting Mean, Variance, and Standard Deviation In Exercise, find the (a) mean, (b) variance and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results. Political Correctness Fifty-nine percent of likely U.S. voters think that most school textbooks put political correctness ahead of accuracy. You randomly select seven likely U.S. voters and ask them whether they think that most school textbooks put political correctness ahead of accuracy. The random variable represents the number of likely U.S. voters who think that most school textbooks put political correctness ahead of accuracy.

Problem 29E Finding and Interpreting Mean, Variance, and Standard Deviation In Exercise, find the (a) mean, (b) variance and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results. Life on Mars Thirty-one percent of adults think that life existed on Mars at some point in time. You randomly select six adults and ask them whether they think life existed on Mars at some point in time. The random variable represents the number of adults who think that life existed on Mars at some point in time.

Problem 32E Finding and Interpreting Mean, Variance, and Standard Deviation In Exercise, find the (a) mean, (b) variance and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results. Supreme Court Sixty-three percent of adults cannot name a Supreme Court justice. You randomly select five adults and ask them whether they can name a Supreme Court justice. The random variable represents the number of adults who cannot name a Supreme Court justice.

Problem 30E Finding and Interpreting Mean, Variance, and Standard Deviation In Exercise, find the (a) mean, (b) variance and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results. World’s Policeman Eleven percent of likely U.S. voters think that the United States should be the world’s policeman. You randomly select five likely U.S. voters and ask them whether they think that the United States should be the world’s policeman. The random variable represents the number of likely U.S. voters who think that the United States should be the world’s policeman.

According to a theory in genetics, when tall and colorful plants are crossed with short and colorless plants, four types of plants will result: tall and colorful, tall and colorless, short and colorful, and short and colorless, with corresponding probabilities of \(\frac{9}{16},\frac{3}{16},\frac{3}{16}\) and \(\frac{1}{16}\). Ten plants are selected. Find the probability that 5 will be tall and colorful, 2 will be tall and colorless, 2 will be short and colorful, and 1 will be short and colorless. ________________ Equation Transcription: Text Transcription: frac{9}{16},frac{3}{16},frac{3}{16} frac{1}{16}

Problem 31E Finding and Interpreting Mean, Variance, and Standard Deviation In Exercise, find the (a) mean, (b) variance and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results. Face of the Company Seventy-nine percent of workers know what their CEO looks like. You randomly select six workers and ask them whether they know what their CEO looks like. The random variable represents the number of workers who know what their CEO looks like.

Problem 21E Finding Binomial Probabilities In Exercise, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Comfortable Retirement Fifty-one percent of workers are confident that they will retire with a comfortable lifestyle. You randomly select 10 workers. Find the probability that the number of workers who are confident that they will retire with a comfortable lifestyle is (a) exactly two, (b) more than two, and (c) between two and five, inclusive.

Problem 2E In a binomial experiment with n trials, what does the random variable measure?

In a binomial experiment, what does it mean to say that each trial is independent of the other trials?

In a binomial experiment with n trials, what does the random variable measure?

Graphical Analysis The histograms shown below represent binomial distributions with the same number of trials n but different probabilities of success p. Match each probability with the correct graph. Explain your reasoning. p = 0.25, p = 0.50, p = 0.75 (a) 0.30 0.10 0 1 2 3 4 5 x 0.40 0.20 P(x) (b) 0.20 0.10 0 1 2 3 4 5 x 0.30 0.40 P(x) (c) 0.10 0 1 2 3 4 5 x

Graphical Analysis The histograms shown below represent binomial distributions with the same probability of success p but different numbers of trials n. Match each value of n with the correct graph. Explain your reasoning. What happens as the value of n increases and p remains the same? n = 4, n = 8, n = 12 (a) 0 2 4 6 8 10 12 x P(x) 0.40 0.30 0.20 0.10 (b) 0.40 0.20 0.30 0.10 0 2 4 6 8 10 12 x P(x) (c) 0 2 4 6 8 10 12 x

Identify the unusual values of x in each histogram in Exercise 3.

Identify the unusual values of x in each histogram in Exercise 4.

Mean, Variance, and Standard Deviation In Exercises 710, find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.n = 50, p = 0.4

Mean, Variance, and Standard Deviation In Exercises 710, find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 84, p = 0.65

Mean, Variance, and Standard Deviation In Exercises 710, find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.n = 124, p = 0.26

Mean, Variance, and Standard Deviation In Exercises 710, find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 316, p = 0.82

Identifying and Understanding Binomial Experiments In Exercises 1114, determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why. Video Games A survey found that 49% of U.S. households own a dedicated game console. Eight U.S. households are randomly selected. The random variable represents the number of U.S. households that own a dedicated game console. (Source: Entertainment Software Association)

Identifying and Understanding Binomial Experiments In Exercises 1114, determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why. Cards You draw five cards, one at a time, from a standard deck. You do not replace a card once it is drawn. The random variable represents the number of cards that are hearts

Identifying and Understanding Binomial Experiments In Exercises 1114, determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why.Lottery A state lottery randomly chooses 6 balls numbered from 1 through 40 without replacement. You choose six numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery.

Identifying and Understanding Binomial Experiments In Exercises 1114, determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why.Generation A survey found that 68% of adults ages 18 to 25 think that their generation is unique and distinct. Twelve adults ages 18 to 25 are randomly selected. The random variable represents the number of adults ages 18 to 25 who think that their generation is unique and distinct. (Source: Pew Research Center)

Finding Binomial Probabilities In Exercises 1522, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities.Fair and Accurate News Sixty percent of U.S. adults trust national newspapers to present the news fairly and accurately. You randomly select nine U.S. adults. Find the probability that the number of U.S. adults who trust national newspapers to present the news fairly and accurately is (a) exactly five, (b) at least six, and (c) less than four. (Source: Harris Interactive)

Finding Binomial Probabilities In Exercises 1522, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities.. Childhood Obesity Thirty-nine percent of U.S. adults think that the government should help fight childhood obesity. You randomly select six U.S. adults. Find the probability that the number of U.S. adults who think that the government should help fight childhood obesity is (a) exactly two, (b) at least four, and (c) less than three. (Source: Rasmussen Reports)

Finding Binomial Probabilities In Exercises 1522, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities.Ease of Voting Twenty-seven percent of likely U.S. voters think that it is too easy to vote in the United States. You randomly select 12 likely U.S. voters. Find the probability that the number of likely U.S. voters who think that it is too easy to vote in the United States is (a) exactly three, (b) at least four, and (c) less than eight. (Source: Rasmussen Reports)

Finding Binomial Probabilities In Exercises 1522, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities.. Junk Food Sixty-three percent of U.S. adults oppose special taxes on junk food and soda. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who oppose special taxes on junk food and soda is (a) exactly six, (b) at least five, and (c) less than eight. (Source: Rasmussen Reports)

Finding Binomial Probabilities In Exercises 1522, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities.Clothes Shopping Fifty-six percent of men do not look forward to going clothes shopping for themselves. You randomly select eight men. Find the probability that the number of men who do not look forward to going clothes shopping for themselves is (a) exactly five, (b) more than five, and (c) at most five. (Source: Mens Wearhouse)

Finding Binomial Probabilities In Exercises 1522, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Safety Recall Sixty-eight percent of adults would still consider a car brand despite product/safety recalls. You randomly select 20 adults. Find the probability that the number of adults who would still consider a car brand despite product/safety recalls is (a) exactly one, (b) more than one, and (c) at most one. (Source: Deloitte)

Finding Binomial Probabilities In Exercises 1522, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Comfortable Retirement Fifty-one percent of workers are confident that they will retire with a comfortable lifestyle. You randomly select 10 workers. Find the probability that the number of workers who are confident that they will retire with a comfortable lifestyle is (a) exactly two, (b) more than two, and (c) between two and five, inclusive. (Source: Transamerica Center for Retirement Studies)

Finding Binomial Probabilities In Exercises 1522, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities.Environmentally Friendly Products Forty-three percent of adults would pay more for environmentally friendly products. You randomly select 12 adults. Find the probability that the number of adults who would pay more for environmentally friendly products is (a) exactly four, (b) more than four, and (c) between four and eight, inclusive. (Source: BrandSpark International/Better Homes and Gardens American Shopper Study)

Constructing and Graphing Binomial Distributions In Exercises 2326, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning.100th Birthday Sixty-seven percent of adults ages 55 and older want to reach their 100th birthday. You randomly select seven adults ages 55 and older and ask them whether they want to reach their 100th birthday. The random variable represents the number of adults ages 55 and older who want to reach their 100th birthday. (Source: SunAmerica Retirement Re-Set)

Constructing and Graphing Binomial Distributions In Exercises 2326, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning.Messy Desk Thirty-eight percent of hiring managers have a negative view of workers with a messy desk. You randomly select 10 hiring managers and ask them whether they have a negative view of workers with a messy desk. The random variable represents the number of hiring managers who have a negative view of workers with a messy desk. (Source: CareerBuilder)

Constructing and Graphing Binomial Distributions In Exercises 2326, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning.Work Performance Forty-six percent of working mothers say that their work performance is the same as it was before giving birth. You randomly select eight working mothers and ask them how their work performance has changed since giving birth. The random variable represents the number of working mothers who say that their work performance is the same as it was before giving birth. (Source: Forbes)

Constructing and Graphing Binomial Distributions In Exercises 2326, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning. . School Standards Thirty-four percent of voters think that Congress should help write standards for school food. You randomly select six voters and ask them whether Congress should help write standards for school food. The random variable represents the number of voters who think that Congress should help write standards for school food. (Source: Hart Research Associates/ American Viewpoint for Kids Safe & Healthful Foods Project)

Finding and Interpreting Mean, Variance, and Standard Deviation In Exercises 2732, find the (a) mean, (b) variance and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results. Political Correctness Fifty-nine percent of likely U.S. voters think that most school textbooks put political correctness ahead of accuracy. You randomly select seven likely U.S. voters and ask them whether they think that most school textbooks put political correctness ahead of accuracy. The random variable represents the number of likely U.S. voters who think that most school textbooks put political correctness ahead of accuracy. (Source: Rasmussen Reports)

Finding and Interpreting Mean, Variance, and Standard Deviation In Exercises 2732, find the (a) mean, (b) variance and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results.Potentially Offensive Songs Sixty-nine percent of adults think that musicians should be allowed to sing potentially offensive songs. You randomly select four adults and ask them whether they think musicians should be allowed to sing potentially offensive songs. The random variable represents the number of adults who think musicians should be allowed to sing potentially offensive songs. (Source: First Amendment Center)

Finding and Interpreting Mean, Variance, and Standard Deviation In Exercises 2732, find the (a) mean, (b) variance and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results.. Life on Mars Thirty-one percent of adults think that life existed on Mars at some point in time. You randomly select six adults and ask them whether they think life existed on Mars at some point in time. The random variable represents the number of adults who think that life existed on Mars at some point in time. (Source: CNN/ORC Poll)

Finding and Interpreting Mean, Variance, and Standard Deviation In Exercises 2732, find the (a) mean, (b) variance and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results.Worlds Policeman Eleven percent of likely U.S. voters think that the United States should be the worlds policeman. You randomly select five likely U.S. voters and ask them whether they think that the United States should be the worlds policeman. The random variable represents the number of likely U.S. voters who think that the United States should be the worlds policeman. (Source: Rasmussen Reports)

Finding and Interpreting Mean, Variance, and Standard Deviation In Exercises 2732, find the (a) mean, (b) variance and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results.Face of the Company Seventy-nine percent of workers know what their CEO looks like. You randomly select six workers and ask them whether they know what their CEO looks like. The random variable represents the number of workers who know what their CEO looks like. (Source:

Finding and Interpreting Mean, Variance, and Standard Deviation In Exercises 2732, find the (a) mean, (b) variance and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results.Supreme Court Sixty-three percent of adults cannot name a Supreme Court justice. You randomly select five adults and ask them whether they can name a Supreme Court justice. The random variable represents the number of adults who cannot name a Supreme Court justice. (Source:

Multinomial Experiments In Exercises 33 and 34, use the information below. A multinomial experiment is a probability experiment that satisfies these conditions. 1. The experiment has a fixed number of trials n, where each trial is independent of the other trials. 2. Each trial has k possible mutually exclusive outcomes: E1, E2, E3, . . ., Ek . 3. Each outcome has a fixed probability. So, P1E12 = p1, P1E22 = p2, P1E32 = p3, . . ., P1Ek2 = pk. The sum of the probabilities for all outcomes is p1 + p2 + p3 + g+ pk = 1. 4. The number of times E1 occurs is x1, the number of times E2 occurs is x2, the number of times E3 occurs is x3, and so on. 5. The discrete random variable x counts the number of times x1, x2, x3, . . ., xk occur in n independent trials where x1 + x2 + x3 + g+ xk = n. The probability that x will occur is P1x2 = n! x1!x2!x3! gxk! p1 x1 p2 x2 p3 x3gpk xk.Genetics According to a theory in genetics, when tall and colorful plants are crossed with short and colorless plants, four types of plants will result: tall and colorful, tall and colorless, short and colorful, and short and colorless, with corresponding probabilities of 9 16, 3 16, 3 16, and 1 16. Ten plants are selected. Find the probability that 5 will be tall and colorful, 2 will be tall and colorless, 2 will be short and colorful, and 1 will be short and colorless.

Multinomial Experiments In Exercises 33 and 34, use the information below. A multinomial experiment is a probability experiment that satisfies these conditions. 1. The experiment has a fixed number of trials n, where each trial is independent of the other trials. 2. Each trial has k possible mutually exclusive outcomes: E1, E2, E3, . . ., Ek . 3. Each outcome has a fixed probability. So, P1E12 = p1, P1E22 = p2, P1E32 = p3, . . ., P1Ek2 = pk. The sum of the probabilities for all outcomes is p1 + p2 + p3 + g+ pk = 1. 4. The number of times E1 occurs is x1, the number of times E2 occurs is x2, the number of times E3 occurs is x3, and so on. 5. The discrete random variable x counts the number of times x1, x2, x3, . . ., xk occur in n independent trials where x1 + x2 + x3 + g+ xk = n. The probability that x will occur is P1x2 = n! x1!x2!x3! gxk! p1 x1 p2 x2 p3 x3gpk xk.Genetics Another proposed theory in genetics gives the corresponding probabilities for the four types of plants described in Exercise 33 as 5 16, 4 16, 1 16, and 6 16. Ten plants are selected. Find the probability that 5 will be tall and colorful, 2 will be tall and colorless, 2 will be short and colorful, and 1 will be short and colorless.