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Question

About 8% of males are colorblind. A researcher needs some colorblind subjects for an experiment and begins checking potential subjects. What's the probability that she finds someone who is colorblind before checking the 10th man?

Solution

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Given:

n=9n=9

p=8%=0.08p=8\%=0.08

The distribution of a variable that measures the number of successes is a binomial distribution.

Definition binomial probability:

P(X=k)=(nk)pk(1p)nkP(X=k)=\left( \begin{matrix} n \\ k \end{matrix}\right)\cdot p^k\cdot (1-p)^{n-k}

Then we obtain

P(X=0)=(90)0.080(10.08)900.4722P(X=0)=\left( \begin{matrix} 9 \\ 0 \end{matrix}\right)\cdot 0.08^0\cdot (1-0.08)^{9-0}\approx 0.4722

Use the complement rule:

P(X>0)=1P(X=0)=10.4722=0.5278=52.78%P(X>0)=1-P(X=0)=1-0.4722=0.5278=52.78\%

Command Ti83/84-calculator: 1-binompdf(9,0.08,0)

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