Question

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

Answer 1

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.

Answer 2

Answer:

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