Answer to Question #203543 in Statistics and Probability for ask

Question

Suppose a researcher goes to a small college of 200 faculty, 12 of which have blood type O-negative. He obtains a simple random sample of n = 20 of the faculty. Let the random variable X represent the number of faculty in the sample of size that have blood type O-negative.

(a) What is the probability that 3 of the faculty have blood type O-negative? (Round your answer to the nearest thousandth).    

(b)  What is the probability that a none (x = 0) of the faculty has blood type O-negative? (Round your answer to the nearest thousandth).

Answer 1

$n=20 \\ p=\frac{12}{200}=0.06 \\ q=1-0.06=0.94 \\ (a) \; P(X=3) = \frac{20!}{3!(20-3)!}(0.06)^3(0.94)^{20-3} \\ = \frac{6840}{6} \times 0.000216 \times 0.349279 \\ =0.086 \\ (b) \; P(X=0) = \frac{20!}{0!(20-0!}(0.06)^0(0.94)^{20-0} \\ = 1 \times 1 \times 0.94^{20} \\ = 0.290$