in a class of students, the following data table summarizes how many students play an instrument or a sport…
in a class of students, the following data table summarizes how many students play an instrument or a sport. what is the probability that a student plays an instrument given that they play a sport?\n| |plays an instrument|does not play an instrument|\n|--|--|--|\n|plays a sport|3|11|\n|does not play a sport|2|9|
Answer
Explanation:
Step1: Recall conditional - probability formula
The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if $A$ is the event of playing an instrument and $B$ is the event of playing a sport, then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of students who play an instrument and a sport, and $n(B)$ is the number of students who play a sport.
Step2: Identify relevant values from the table
From the table, the number of students who play an instrument and a sport $n(A\cap B) = 3$, and the number of students who play a sport $n(B)=3 + 11=14$.
Step3: Calculate the probability
$P(A|B)=\frac{n(A\cap B)}{n(B)}=\frac{3}{14}$.
Answer:
$\frac{3}{14}$