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.