Question

There are 12 boys and 18 girls in Mr. Spano's math class. If he randomly calls on three students for answers to an assignment, what is the probability that all three are girls? Assume he does not call on the same student more than once.

Answer 1

Answer: 0.737.

Explanation:

Step-1: Find the total number of possible combinations of 3 students that Mr. Spano can choose.

There are 30 students in the class. To find the total number of combinations, we can use the formula nCr = n! / r! (n - r)!

nCr = 30C3

nCr = 30! / 3! (30 - 3)!

nCr = 30!/3!(27!)

nCr = 1140

Step-2: Find the total number of combinations where all 3 students are girls.

There are 18 girls in the class. To find the total number of combinations, we can use the same formula as before:

gC3 = 18C3

gC3 = 18! / 3! (18 - 3)!

gC3 = 18!/3!(15!)

gC3 = 840

Step-3: Compute the probability that all three students are girls.

To compute the probability, we use the following formula:

P(girls) = gC3 / nCr

P(girls) = 840/1140

P(girls) = 0.737

Therefore, the probability that all 3 students Mr. Spano calls on are girls is 0.737.