Answer to Question #342782 in Statistics and Probability for Zain

Question

Suppose a researcher goes to a small college of 200 faculty, 12 of which have blood type O-negative. She obtains a simple random sample 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?

b. What is the probability that at least one of the faculty has blood type O-negative?

Answer 1

Let $X=$ the number of faculty who have blood type O-negative: $X\sim Bin (n, p).$

Given $p=12/200=0.06, q=1-p=0.94, n=20.$

a.

$$P(X=3)=\dbinom{20}{3}(0.06)^{3}(0.94)^{20-3}$$

$$=0.08600666617$$

b.

$$P(X\ge1)=1-P(X=0)$$

$$=1-\dbinom{20}{0}(0.06)^{0}(0.94)^{20-0}$$

$$=0.70989375886$$