Question

A recent study by the American Accounting Association revealed among 30 graduates in accounting 20 students graduating with a major in accounting select public accounting. Suppose we select a sample of 15 recent graduates.

A. What is the probability that exactly two select public accounting?

B. What is the probability that exactly five select public accounting?

Answer 1

Let $X=$the number of students who $X\sim Bin(n, p)$

Given $n=15, p=\dfrac{2}{3}, q=1-p=\dfrac{1}{3}$

A.

$$P(X=2)=\dbinom{15}{2}(\dfrac{2}{3})^2(\dfrac{1}{3})^{15-2}$$

$$\approx0.000029$$

B.

$$P(X=5)=\dbinom{15}{5}(\dfrac{2}{3})^5(\dfrac{1}{3})^{15-5}$$

$$\approx0.006697$$