Approximately 8.33% of men are colorblind. You survey men from a large populatio

Question

Approximately 8.33% of men are colorblind. You survey men from a large population until you find one who is colorblind. Let X = the number of men you survey up-to-and-including the first man who is colorblind.
a) Explain in words why X has a geometric distribution; what is the success probability?

b) What is the probability that you will have to survey at most 16 men until you find the first one who is colorblind? (Answer: = 0:75.)

c) What is the probability you will have to ask exactly 12 men until you nd the first who is colorblind? (Answer: = 0:032)

d) What is the expected value of X? (Answer: = 12.)

Explanation / Answer

a)as we need to continue till we meet our result, therefore it is geometric distribution where number of trails are not fixed.

success probability=0.0833

b) probability that you will have to survey at most 16 men until you find the first one who is colorblind

=1-P(till 16 men you do not found any) =1-(1-0.0833)16 =0.75132

c)probability you will have to ask exactly 12 men until you nd the first who is colorblind=P(first 11 men not blind*12 men is) =(1-0.0833)11*0.0833 =0.0319996

d)expected value=1/p=1/0.0833=12

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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