Answer: Independent and Dependent Events. In Exercises 512, (a) determine whether events

Notation Let R be the event of randomly selecting a senator and getting a Republican, and let D represent the event of randomly selecting a second different senator and getting a Democrat. Use words to describe what the notation P ( D | R ) represents.

Independent and Dependent Events Are events R and D from Exercise 1 independent or dependent? Explain.

Independent and Dependent Events True or false: The event of finding that your car's radio works and the event of finding that your car's air conditioner works are independent events because they work separately from each other. Explain

Sample for a Poll There are currently 28,741,346 adults in California, and they are all included in one large numbered list. The Gallup organization uses a computer to randomly select 1068 different numbers between 1 and 28,741,346 and then contacts the corresponding adults for a survey. Are the events of selecting the adults actually independent or dependent? If the events are dependent, can they be treated as being independent for the purposes of calculations?

Independent and Dependent Events. In Exercises 512, (a) determine whether events A and B are independent or dependent, and (b) find P(A and B), the probability that events A and B both occur .A: When a month is randomly selected and ripped from a calendar and destroyed, it is July. B: When a different month is randomly selected and ripped from a calendar, it is November.

Independent and Dependent Events. In Exercises 512, (a) determine whether events A and B are independent or dependent, and (b) find P(A and B), the probability that events A and B both occur .A: When a baby is born, it is a girl. B: When a second baby is born into a different family, it is also a girl.

Independent and Dependent Events. In Exercises 512, (a) determine whether events A and B are independent or dependent, and (b) find P(A and B), the probability that events A and B both occur .A: When a baby is born, it is a girl. B: When a single die is rolled, the outcome is 6.

Independent and Dependent Events. In Exercises 512, (a) determine whether events A and B are independent or dependent, and (b) find P(A and B), the probability that events A and B both occur .A: When a day of the week is randomly selected, it is a Saturday. B: When a second different day of the week is randomly selected, it is a Monday

Independent and Dependent Events. In Exercises 512, (a) determine whether events A and B are independent or dependent, and (b) find P(A and B), the probability that events A and B both occur .A: When one of the 222 coins listed in Data Set 21 is randomly selected, it is one of the 5 Indian pennies. B: When another one of the 222 coins listed in Data Set 21 is randomly selected, it is also one of the 5 Indian pennies.

Independent and Dependent Events. In Exercises 512, (a) determine whether events A and B are independent or dependent, and (b) find P(A and B), the probability that events A and B both occur .. A: When the first digit (0 through 9) of a fourdigit lottery number is chosen by someone buying a ticket, it is the same first digit that is later drawn in the official lottery. B: When the second digit of a fourdigit lottery number is chosen by someone buying a ticket, it is the same second digit that is later drawn in the official lottery

Independent and Dependent Events. In Exercises 512, (a) determine whether events A and B are independent or dependent, and (b) find P(A and B), the probability that events A and B both occur .A: When a survey subject is randomly selected from the 100 senators in the 111th Congress, it is one of the 58 Democrats. B: When a second different senator is randomly selected, it is the one senator who is an Independent.

Independent and Dependent Events. In Exercises 512, (a) determine whether events A and B are independent or dependent, and (b) find P(A and B), the probability that events A and B both occur .A: When an M&M is randomly selected from the 100 M&Ms listed in Data Set 20, it is one of the 8 yellow M&Ms. B: When a second different M&M is randomly selected from those listed in Data Set 20, it is also a yellow M&M.

PreEmployment Drug Screening. In Exercises 1316, use the test results summarized in Table 41, reproduced here. Consider an event to be unlikely if its probability is 0.05 or less. Table 41 PreEmployment Drug Screening Results Positive Test Result (Drug Use Is Indicated) Negative Test Result (Drug Use Is Not Indicated) Subject Uses Drugs 44 (True Positive) 6 (False Negative) Subject Is Not a Drug User 90 (False Positive) 860 (True Negative)PreEmployment Drug Screening If 2 of the 1000 test subjects are randomly selected, find the probability that they both had false positive results. Is it unlikely to randomly select 2 subjects and get 2 results that are both false positive results? a. Assume that the 2 selections are made with replacement. b. Assume that the 2 selections are made without replacement.

PreEmployment Drug Screening. In Exercises 1316, use the test results summarized in Table 41, reproduced here. Consider an event to be unlikely if its probability is 0.05 or less. Table 41 PreEmployment Drug Screening Results Positive Test Result (Drug Use Is Indicated) Negative Test Result (Drug Use Is Not Indicated) Subject Uses Drugs 44 (True Positive) 6 (False Negative) Subject Is Not a Drug User 90 (False Positive) 860 (True Negative)PreEmployment Drug Screening If 3 of the 1000 test subjects are randomly selected, find the probability that they all had false negative results. Is it unlikely to randomly select 3 subjects and get 3 results that are all false negative results? a. Assume that the 3 selections are made with replacement. b. Assume that the 3 selections are made without replacement

PreEmployment Drug Screening. In Exercises 1316, use the test results summarized in Table 41, reproduced here. Consider an event to be unlikely if its probability is 0.05 or less. Table 41 PreEmployment Drug Screening Results Positive Test Result (Drug Use Is Indicated) Negative Test Result (Drug Use Is Not Indicated) Subject Uses Drugs 44 (True Positive) 6 (False Negative) Subject Is Not a Drug User 90 (False Positive) 860 (True Negative)PreEmployment Drug Screening If 3 of the 1000 test subjects are randomly selected, find the probability that they all had correct test results (either true positive or true negative). Is such an event unlikely? a. Assume that the 3 selections are made with replacement. b. Assume that the 3 selections are made without replacement.

PreEmployment Drug Screening. In Exercises 1316, use the test results summarized in Table 41, reproduced here. Consider an event to be unlikely if its probability is 0.05 or less. Table 41 PreEmployment Drug Screening Results Positive Test Result (Drug Use Is Indicated) Negative Test Result (Drug Use Is Not Indicated) Subject Uses Drugs 44 (True Positive) 6 (False Negative) Subject Is Not a Drug User 90 (False Positive) 860 (True Negative)PreEmployment Drug Screening If 4 of the 1000 test subjects are randomly selected, find the probability that they all had true negative test results. Is such an event unlikely? a. Assume that the 4 selections are made with replacement. b. Assume that the 4 selections are made without replacement.

Acceptance Sampling With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device (based on data from Pacemaker and ICD Generator Malfunctions, by Maisel et al., Journal of the American Medical Association, Vol. 295, No. 16). If the firmware is tested in three different pacemakers randomly selected from this batch of 8834, what is the probability that the firmware in the entire batch will be accepted? Does this procedure suggest that the entire batch consists of good pacemakers? Why or why not?

Acceptance Sampling With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. Among 810 airport baggage scales, 102 are defective (based on data from the New York City Department of Consumer Affairs). If four of the scales are randomly selected and tested, what is the probability that the entire batch will be accepted? Is this scheme likely to detect the large number of defects?

Redundancy in Computer Hard Drives It is generally recognized that it is wise to back up computer data. Assume that there is a 2% rate of disk drive failure in a year (based on data fom various sources, including Failure Trends in Large Disk Drive Population, by Pinhero et al. of Google, Inc.). a. If you store all of your computer data on a single hard disk drive, what is the probability that the drive will fail during a year? b. If all of your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that both drives will fail during a year? c. If copies of all of your computer data are stored on three independent hard disk drives, what is the probability that all three will fail during a year? d. Describe the improved reliability that is gained with backup drives.

Redundancy in Aircraft Radios The FAA requires that commercial aircraft used for flying in instrument conditions must have two independent radios instead of one. Assume that for a typical flight, the probability of a radio failure is 0.0035. What is the probability that a particular flight will be threatened with the failure of both radios? Describe how the second independent radio increases safety in this case.

. Born on the 4th of July For the following, ignore leap years and assume that births on the 365 different days of the year are equally likely. a. What is the probability that a randomly selected person was born on July 4? b. What is the probability that two randomly selected people were both born on July 4? c. What is the probability that two randomly selected people were born on the same day?

Hiring Employees Assume that Google, Inc. hires employees on the different business days of the week (Monday through Friday) with equal likelihood. a. If two different employees are randomly selected, what is the probability that they were both hired on a Monday? b. If two different employees are randomly selected, what is the probability that they were both hired on the same day of the week? c. What is the probability that 10 people in the same department were all hired on the same day of the week? Is such an event unlikely?

In Exercises 2326, use these results from the 1PanelTHC test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 41, which is included with the Chapter Problem.). Screening for Marijuana Use If 2 of the subjects are randomly selected without replacement, what is the probability that they both had correct test results (either true positive or true negative)? Is such an event unlikely?

In Exercises 2326, use these results from the 1PanelTHC test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 41, which is included with the Chapter Problem.)Screening for Marijuana Use If 2 of the subjects are randomly selected without replacement, what is the probability that they both had incorrect test results (either false positive or false negative)? Is such an event unlikely?

In Exercises 2326, use these results from the 1PanelTHC test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 41, which is included with the Chapter Problem.)Screening for Marijuana Use If 3 of the subjects are randomly selected without replacement, what is the probability that they all had false positive test results? Is such an event unlikely?

In Exercises 2326, use these results from the 1PanelTHC test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 41, which is included with the Chapter Problem.)Screening for Marijuana Use If 3 of the subjects are randomly selected without replacement, what is the probability that they all had true negative test results? Is such an event unlikely?

In Exercises 2730, find the probabilities and indicate when the 5% guideline for cumbersome calculations is used.Road Rage In a Prince Market Research survey of 2518 motorists, 252 said that they made an obscene gesture in the previous month. a. If 1 of the surveyed motorists is randomly selected, what is the probability that this motorist did not make an obscene gesture in the previous month? b. If 50 of the surveyed motorists are randomly selected without replacement, what is the probability that none of them made an obscene gesture in the previous month?

In Exercises 2730, find the probabilities and indicate when the 5% guideline for cumbersome calculations is used.Flirting In a Microsoft Instant Messaging survey, 1021 adults were asked to identify the most fun way to flirt, and 61of them chose email. a. If 1 of the surveyed adults is randomly selected, what is the probability that this person chose something other than email? b. If 40 of the different subjects are randomly selected without replacement, what is the probability that each of them chose something other than email?

In Exercises 2730, find the probabilities and indicate when the 5% guideline for cumbersome calculations is used.Online Shopping Survey 427 different adult women were randomly selected and asked what they purchase online, and 162 of the women said that they purchase clothes online (based on a survey by the Consumer Reports Research Center). a. If 2 of the surveyed women are randomly selected without replacement, what is the probability that they both chose the category of clothing? b. If 10 different surveyed women are randomly selected without replacement, what is the probability that none of them chose the category of clothing?

In Exercises 2730, find the probabilities and indicate when the 5% guideline for cumbersome calculations is used.Airline Survey Among respondents asked which is their favorite seat on a plane, 492 chose the window seat, 8 chose the middle seat, and 306 chose the aisle seat (based on data from USA Today). a. What is the probability of randomly selecting 1 of the surveyed people and getting one who did not choose the middle seat? b. If 2 of the surveyed people are randomly selected without replacement, what is the probability that neither of them chose the middle seat? c. If 25 different surveyed people are randomly selected without replacement, what is the probability that none of them chose the middle seat?

System Reliability Refer to the figure at the top of the next page in which surge protectors p and q are used to protect an expensive 3D HDTV. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.99 probability of working correctly when a voltage surge occurs. a. If the two surge protectors are arranged in series, what is the probability that a voltage surge will not damage the television? (Do not round the answer.) b. If the two surge protectors are arranged in parallel, what is the probability that a voltage surge will not damage the television? (Do not round the answer.)c. Which arrangement should be used for the better protection?

Same Birthdays If 25 people are randomly selected, find the probability that no 2 of them have the same birthday. Ignore leap years.