About 8 % of all men are colorblind. Suppose we randomly select men 1 by 1 from

Question

About 8 % of all men are colorblind. Suppose we randomly select men 1 by 1 from a large population. Let X = the number of men we select until we find the first one who is colorblind a. What type of probability distribution does X have? (That is what is its name?) b. What is the probability that we find the 1st colorblind man on the 12th selection? c. What is the probability that we find the 1st colorblind man by the 12th selection? d. What is the probability that it takes more than 12 selections to find the 1st colorblind man? e. What is the probability that we must examine exactly 20 non-colorblind men before we examine the 2nd colorblind man?f. What is the expected value of X? g. What is the variance of X? h. What is the variance of 7X + 3?

Explanation / Answer

As multiple parts are posted, only the first 4 will be answered.

a. X has a geometric distribution with p = 0.08

b. P(X=12) = No success in 1st 11 attempts * success in 12th attempt

= (1-0.08)12-1 * 0.08 = 0.0320

c. Probability that we find the 1st colorblind man by the 12th selection = P(X<=12) = 1 - P(X>12)

= All of the 1st 12 attempts fail = (1-0.08)12 = 0.3677

d. Probability that it takes more than 12 selections to find the 1st colorblind man = P(X>12)

= 1 - P(X<=12) = 1 - 0.3677 = 0.6323

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.