a skating rink attendant monitored the number of injuries at the rink over the past year. he tracked the…

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.\n| |in - line skates|roller skates|\n|--|--|--|\n|minors|5|6|\n|adults|8|6|\n|seniors|12|13|\nwhat is the probability that a randomly selected injured skater was a senior given that the injured skater was wearing in - line skates?\nsimplify any fractions.

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.\n| |in - line skates|roller skates|\n|--|--|--|\n|minors|5|6|\n|adults|8|6|\n|seniors|12|13|\nwhat is the probability that a randomly selected injured skater was a senior given that the injured skater was wearing in - line skates?\nsimplify any fractions.

Answer

Explanation:

Step1: Calculate total in - line skaters

Add up the number of minors, adults, and seniors wearing in - line skates. $5 + 8+12=25$.

Step2: Identify number of senior in - line skaters

The number of seniors wearing in - line skates is 12.

Step3: Calculate the conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In this case, the probability that a skater is a senior given they are wearing in - line skates is the number of senior in - line skaters divided by the total number of in - line skaters. So the probability is $\frac{12}{25}$.

Answer:

$\frac{12}{25}$