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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?

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Given:

$n=9$

$p=8\%=0.08$

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

Definition binomial probability:

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

Then we obtain

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

Use the complement rule:

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

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

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