Question

A skating rink attendant monitored the number of injuries at the rink over the past year. He tracked the ages of those injured and the kinds of skates worn during injury. In-line skates Roller skates Age 8 4 2 Age 10 5 3 What is the probability that a randomly selected injured skater was wearing roller skates given that the injured skater was age 8? Simplify any fractions.

Answer 1

Solution

We have the following info:

In-line Roller skates Total

Age 8 4 2 6

Age 10 5 3 8

__________________________________

Total 9 5 14

For this case we can define the following events:

A= the skater belong roller skates

B= the skate is at age 8

And we want to find this probability:

$P(A|B)=\frac{P(\text{AandB)}}{P(B)}$

And we can do this:

P(A and B) = 2/14

P(B)= 6/14

Replacing we got:

$P(A|B)=\frac{\frac{2}{14}}{\frac{6}{14}}=\frac{2}{6}=\frac{1}{3}$