Question

There are four boys and 8 girls on the debate team. the coach randomly chooses 3 of the students to participate in a competition. what is the probability the coach selects all girls?

Answer 1

The probability that the coach selects all girls from the debate team can be calculated using the concept of hypergeometric probability. Using the given number of girls and boys in the team, the probability is found to be 1/22.

Step-by-step explanation:

The probability that the coach selects all girls can be calculated using the concept of hypergeometric probability. The group of interest is the 3 students selected by the coach, while the sample consists of all 12 girls and 4 boys on the debate team.

To calculate the probability, we use the formula for hypergeometric probability:

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

Where:

P(X = k) = probability of selecting k girls

C(k, m) = number of ways to choose k girls from m girls

C(n - k, N - m) = number of ways to choose (n - k) boys from (N - m) total students

C(n, N) = number of ways to choose n students from N total students

In this case, we want to find the probability of selecting all 3 girls, so k = 3, m = 8, n = 3, and N = 12 + 4 = 16.

Plugging in the values into the formula:

P(X = 3) = (C(3, 8) * C(0, 4))/(C(3, 12))

Simplifying the equation:

P(X = 3) = (1 * 1)/(22) = 1/22

Therefore, the probability that the coach selects all girls is 1/22.

Answer 2

the probability the coach selects all girls is most likely