The table shows the number of championships won by the baseball and softball leagues of three youth baseball divisions organized by age groups.

Baseball League (B) Softball League (S)

Ages 7 - 9 (X) 3 7

Ages 10 - 12 (Y) 2 2

Ages 13 - 15 (Z) 1 1

Given that the winning team is a member of the softball league, find the probability that the winner is in the Ages 7 - 9 division. Answer in terms of a reduced fraction.

P (X|S) =

a0

a1

The correct answer is:

7/10

Explanation:

Finding the totals of each column and row, we find:

There are 3+2+1 = 6 children in the baseball league.

There are 7+2+1 = 10 children in the softball league.

There are 3+7 = 10 children in the 7-9 division.

There are 2+2 = 4 children in the 10-12 division.

There are 1+1 = 2 children in the 13-15 division.

There are a total of 10+6 = 16 children.

We start with the information that the team is a member of the softball league. There are 10 children in this league; this is the denominator of the probability.

There are 7 children in the 7-9 division that are in the softball league. This gives us the probability 7/10.

The first blank spot would be 7 and the last one is 10.