A math class consists of 38 students, 24 female and 14 male. Three students are selected at random, one at a time, to participate in a probability experiment (selected in order without replacement).

Question

A. What is the probability that a male is selected, then two females?

B. What is the probability that a female is selected, then two males?

C. What is the probability that two females are selected, then one male?

D. What is the probability that three males are selected?

E. What is the probability that three females are selected?

Answer 1

There are a total of 38 students (24 females and 14 males). We will select 3 students randomly without replacement. Use the probability of combinations.

P(3 males) = C(14,3)/C(38,3) = 364/8436 = 0.04315

The probability that 3 males are selected is 0.04315.

P(3 females) = C(24,3)/C(38,3) = 2024/8436 = 0.23992

The probability that 3 females are selected is 0.23992.

P(1 male then 2 females) = [C(14,1)*C(24,2)]/C(38,3) = (14*276)/8436 = 0.45804

The probability that 1 male is selected and then 2 females are selected is 0.45804.

P(1 female then 2 males) = [C(24,1)*C(14,2)]/C(38,3) = (24*91)/8436 = 0.25889

The probability that 1 female is selected and then 2 males are selected is 0.25889.

P(2 females then 1 male) = [C(24,2)*C(14,1)]/C(38,3) = (276*14)/8436 = 0.45804

The probability that 2 females are selected and then 1 male is selected is 0.45804.