2. 60 points Some biology students were checking the eye color of 10 fruit fies

Question

2. 60 points Some biology students were checking the eye color of 10 fruit fies For the individual fly, suppose that the probability of white eyes is 0.6 and tie probability of red eyes is 0.4, and that we may treat these observations as inde pendent Bernoulli trials. Let X be the number of flies with white eyes among the 10 fies that we will observe. (a)20 points What is the probability that exactly 5 fies will have white eyes? (b) 20 points What is the probability that at least one fly will have white eyes 2 polinh Whiat i te and te i

Explanation / Answer

X ~ B(n,p)

Where n = 10, p = 0.6

n-bernoulli (binomial) probability distribution is

P(X) = nCx px ( 1 - p)n-x

a)

P( X = 5) = 10C5 0.605 0.405

= 0.20066

b)

P( at least 1) = P( X >= 1)

P( X >= 1) = 1 - P( X = 0)

= 1 - 10C0 0.600 0.4010

= 0.999895

c)

Mean E(X) = np = 10 * 0.6 = 6

Variance (X) = np(1-p) = 10 * 0.6 * 0.4 = 2.4

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