Approximately 8.88% of men are colorblind. You survey men from a large populatio

Question

Approximately 8.88% of men are colorblind. You survey men from a large population until you find one who is colorblind. (Think about what kind of distribution this is) a) What is the probability you will have to survey at most 15 men until you find the first one who is colorblind? b) What is the probability you will have to ask exactly 11 men until you find the first one who is colorblind? c) What is the expected value of X? d) What is the variance of X? Approximately 8.88% of men are colorblind. You survey men from a large population until you find one who is colorblind. (Think about what kind of distribution this is) a) What is the probability you will have to survey at most 15 men until you find the first one who is colorblind? b) What is the probability you will have to ask exactly 11 men until you find the first one who is colorblind? c) What is the expected value of X? d) What is the variance of X? Approximately 8.88% of men are colorblind. You survey men from a large population until you find one who is colorblind. (Think about what kind of distribution this is) a) What is the probability you will have to survey at most 15 men until you find the first one who is colorblind? b) What is the probability you will have to ask exactly 11 men until you find the first one who is colorblind? c) What is the expected value of X? d) What is the variance of X? a) What is the probability you will have to survey at most 15 men until you find the first one who is colorblind? b) What is the probability you will have to ask exactly 11 men until you find the first one who is colorblind? c) What is the expected value of X? d) What is the variance of X?

Explanation / Answer

Here p = 0.088

(a) Required probability = 1 - (1-p)^15 = 1 - (1-0.088)^15 = 0.7489

(b) Required probability = (1-p)^10 * p = (1-0.088)^10*0.088 = 0.035

(c) expected value = 1/p = 1/0.088 = 11.3636

(d) variance of x = (1-p)/p^2 = (1-0.088)/0.088^2 = 117.7686

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