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12.Fruit Flies An experiment with fruit flies involves one parent with normal wings and one parent with vestigial wings. When these parents have an offspring, there is a 3/4 probability that the offspring has normal wings and a 1/4 probability of vestigial wings. If the parents give birth to five offspring, what is the probability that at least one of the offspring has vestigial wings? If researchers need at least one offspring with vestigial wings, can they be quite confident of getting one?

Question

12.Fruit Flies An experiment with fruit flies involves one parent with normal wings and one parent with vestigial wings. When these parents have an offspring, there is a 3/4 probability that the offspring has normal wings and a 1/4 probability of vestigial wings. If the parents give birth to five offspring, what is the probability that at least one of the offspring has vestigial wings? If researchers need at least one offspring with vestigial wings, can they be quite confident of getting one?

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Step 1

Consider events A and B as an offspring has vestigial wings and an offspring having normal wings.

P(A) p
1
4
-0.25
P(B) q
3
4
0.75
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P(A) p 1 4 -0.25 P(B) q 3 4 0.75

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Step 2

Consider X be a random variable that follows binomial distribution indicates the number of off spring that has vestigial wings. The t...

P(X21) P(X 1)+ P(X 2)+P(X = 3)+ P(X 4)+P (X = 5)
-1-P(X 0)
=1- "C,pq
1-c,(025) (0.75)
1-0.2373
=0.7627
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P(X21) P(X 1)+ P(X 2)+P(X = 3)+ P(X 4)+P (X = 5) -1-P(X 0) =1- "C,pq 1-c,(025) (0.75) 1-0.2373 =0.7627

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