About 8% of men are colorblind. A researcher needs some colorblind subjects for

Question

About 8% of men are colorblind. A researcher needs some colorblind subjects for an experiment and begins checking potential subjects. Assume the researcher will select four men at random. Address parts (a) – (d). Please report each percentage with at least two digits after the decimal point. Communicate the process you use to get each value.

(a) What is the probability that the fourth man will be colorblind but none of the others will be colorblind?

(b) What is the probability that exactly one of the four men will be colorblind?

(c) What is the probability that all four men will be colorblind?

(d) Now suppose the researcher selects 18 men at random. [Both parts of this problem (part (d)) are optional.]

1. What is the probability that exactly 7 of the 18 men are colorblind?

2. What is the probability that at least 3 of the 18 men are colorblind?

Explanation / Answer

P(color blind) = 0.08, P(Not color blind) = 1 - p = 0.92

(a) Probability = 0.92 * 0.92 * 0.92 * 0.08 = 0.0623

(b) x = 1

P(x) = C(n, x) p^x q^ (n - x)

P(1) = C(4, 1) 0.08^1 0.92^(4 - 1) = 0.2492

(c) x = 4

P(4) = C(4, 4) 0.08^4 0.92^(4 - 4) = 0.00004

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