Question

A team of 7 players is picked from a class of 10 freshmen and 15 sophomores. What is the probability that the team has 3 freshmen and 4 sophomores?

A) 0.0216
B) 0.1429
C) 0.1048
D) 0.2931

Answer 1

The probability that the team has 3 freshmen and 4 sophomores is approximately 0.0216.

Step-by-step explanation:

To find the probability that the team has 3 freshmen and 4 sophomores, we need to calculate the number of ways to select 3 freshmen from a class of 10 and 4 sophomores from a class of 15, and divide it by the total number of ways to select 7 players from a total class of 25.

The number of ways to select 3 freshmen from 10 is calculated by using combinations: C(10, 3) = 120. The number of ways to select 4 sophomores from 15 is calculated by using combinations: C(15, 4) = 1365. The total number of ways to select 7 players from 25 is calculated by using combinations: C(25, 7) = 480700.

Therefore, the probability is given by: P = (120 * 1365) / 480700 ≈ 0.0216.