color blindness appears in 2% of the people in a certain population. how large must a random sample be in order to be 99% certain that a color blind person is included in the sample?
Let X be the random variable number of color blind people in sample.
X ~ Binomial(n = ?, p = 0.02) (assuming a 'large' population).
The smallest integer value of n such that $\displaystyle \Pr(X \geq 1) \geq 0.99 \Rightarrow \Pr(X = 0) \leq 0.01$ is required.
Therefore find the smallest integer solution to $\displaystyle (0.98)^n \leq 0.01$. Trial and error is as good a technique as any.
Hint: I get an answer for n that's larger than 200 but smaller than 300 .......