Question

There are 7 students in a class: 5 boys and 2 girls. If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?

a) 10/35
b) 10/21
c) 10/15
d) 5/7

Answer 1

The probability of selecting exactly 8 boys out of a group of 10 students from a class of 15 boys and 12 girls is 0.

Step-by-step explanation:

The group of interest in this question is 8 boys and 2 girls being chosen out of a total of 15 boys and 12 girls. The sample is the total number of possible groups of 10 students that can be chosen from the entire class. We can use the hypergeometric distribution to calculate the probability. The formula for this distribution is:

P(X = k) = (C(k, m) * C(N - k, n - m)) / C(N, n)

Where:

• P(X = k) is the probability of exactly k boys being chosen
• C(k, m) is the number of ways to choose k boys out of m
• C(N - k, n - m) is the number of ways to choose (10 - k) students that are not boys out of (27 - m)
• C(N, n) is the total number of ways to choose 10 students out of 27

We want to calculate the probability of exactly 8 boys being chosen, so k = 8 and m = 15. Plugging these values into the formula gives:

P(X = 8) = (C(8, 15) * C(27 - 8, 10 - 15)) / C(27, 10)

Simplifying:

P(X = 8) = (0 * C(19, -5)) / C(27, 10)

Since choosing (-5) students is not possible, the probability is 0. Therefore, the probability of 8 boys being chosen is 0.