Question

In a class of 22 students, there are 15 males and 7 females. If a committee of three is randomly selected

a) What is the probability that two are females and one is male?
b) what is the probability that only one if female

Answer 1

To find the probability of selecting two females and one male from a committee of three students, we can use combination formulas to calculate the number of possible committees that meet the given criteria. The probability of two females and one male is the number of committees with two females and one male divided by the total number of possible committees.

Step-by-step explanation:

To find the probability of selecting two females and one male from a committee of three students, we need to find the total number of possible committees and the number of committees that meet the given criteria.

There are a total of 22 students, so the number of possible committees is given by the combination formula: C(22, 3) = 22! / (3! * (22 - 3)!) = 22! / (3! * 19!)

The number of committees with two females and one male can be found by selecting 2 females from the 7 females and 1 male from the 15 males. This is given by the combination formula: C(7, 2) * C(15, 1) = (7! / (2! * (7 - 2)!)) * (15! / (1! * (15 - 1)!))

The probability can then be calculated by dividing the number of committees with two females and one male by the total number of possible committees: P(two females and one male) = (C(7, 2) * C(15, 1)) / (C(22, 3))

To find the probability of only one female in the committee, we need to select 1 female from the 7 females and 2 males from the 15 males. This is given by the combination formula: C(7, 1) * C(15, 2) = (7! / (1! * (7 - 1)!)) * (15! / (2! * (15 - 2)!))

The probability can then be calculated by dividing the number of committees with only one female by the total number of possible committees: P(only one female) = (C(7, 1) * C(15, 2)) / (C(22, 3))