abdul entered his sister into their towns smelly shoe competition. abdul observed contestants of all ages…
abdul entered his sister into their towns smelly shoe competition. abdul observed contestants of all ages proudly strutting around wearing different kinds of smelly shoes. tennis shoes high heels under 18 6 5 18 or older 3 2 what is the probability that a randomly selected contestant is under 18 given that the contestant is wearing tennis shoes? simplify any fractions.
Answer
Explanation:
Step1: Find total number of tennis - shoe wearers
The number of contestants wearing tennis shoes is the sum of those under 18 and 18 or older wearing tennis shoes. So, $6 + 3=9$.
Step2: Find number of under - 18 tennis - shoe wearers
The number of under - 18 contestants wearing tennis shoes is 6.
Step3: Use conditional probability formula
The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if $A$ is the event of being under 18 and $B$ is the event of wearing tennis shoes, then $P(A|B)=\frac{n(A\cap B)}{n(B)}$. Here, $n(A\cap B) = 6$ (under - 18 and wearing tennis shoes) and $n(B)=9$ (wearing tennis shoes). So the probability is $\frac{6}{9}=\frac{2}{3}$.
Answer:
$\frac{2}{3}$