Fundamental Counting Principle and Probability

Question

Use the Fundamental Counting Principle to determine the total number of outcomes and then calculate the probability.

A couple having twins is deciding on names. They narrowed their choices to 5 boy names and 7 girl names. The new fathers parents like only 1 of the boys names and 2 of the girls names. Assuming that the new parents have one child of each gender, what is the probability that the names they choose will make the new grandparents happy?

Answer 1

The couple is having one boy and one girl, so there are 5 possible names for the boy and 7 possible names for the girl, for a total of 5 x 7 = 35 possible pairs of names.

The new father's parents only like 1 of the names for the boy and 2 of the names for the girl, meaning they like 1 x 2 = 2 of the possible pairs of names.

With two "liked" pairs among 35 "possible" pairs, the probability that the new father's parents will like the pair of names they select is 2 / 35, or approximately 0.057.

(Of course simply asking the new father's parents which names they like would make this much easier! :) )