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Solution: Multinomial Experiments In Exercise, use the
Chapter 4, Problem 38E(choose chapter or problem)
Problem 38E
Multinomial Experiments In Exercise, use the information below.
Genetics Another proposed theory in genetics gives the corresponding probabilities for the four types of plants described in Exercise 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.
Exercise
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, P(E1) = p1, P(E2) = p2, P(E3) = p3, . . ., P(Ek) = pk. The sum of the probabilities for all outcomes is
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
The probability that x will occur is
Questions & Answers
QUESTION:
Problem 38E
Multinomial Experiments In Exercise, use the information below.
Genetics Another proposed theory in genetics gives the corresponding probabilities for the four types of plants described in Exercise 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.
Exercise
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, P(E1) = p1, P(E2) = p2, P(E3) = p3, . . ., P(Ek) = pk. The sum of the probabilities for all outcomes is
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
The probability that x will occur is
ANSWER:
Step 1 of 3
Given:
Four types of plant occur with their respective probabilities in a breeding experiment.