Suppose a class of 50 students has 20 males and 30 females T

Suppose a class of 50 students has 20 males and 30 females. The insturctor will pick 1 (different) student to compete in 3 different national competitions--in mathematics, chemistry, and English.

a. What is the probability that there is exactly 1 female student selected?

b. What is the probability that there are at least 2 male students selected?

Solution

Total = 50

Males = 20

Females = 30

a) P(exactly 1 female) = P(1 female , 2 male)

(30C1 * 20C2) / (50C3) = 0.2908 ---> ANSWER

b) P(atleast 2 males) = P(1 f , 2 m) + P(3 m)

P(1 f , 2 m) was found to be 0.2908
P(3 males) = 20C3 * 30C0 / 50C3 = 0.05816

So, P(atleast 2 males) = 0.2908 + 0.05816 = 0.34896 ---> ANSWER