Answer to Question #338582 in Statistics and Probability for Nahom

Question

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

Answer 1

Let $X=$ the number of select public accounting:$X\sim Bin(n, p).$

Given $n=15, p=20/30=2/3, q=1-p=1/3.$

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

$$\approx0.0002927$$