after growing tired of squinting while driving, jackson went shopping for a pair of sunglasses. he tried on…

after growing tired of squinting while driving, jackson went shopping for a pair of sunglasses. he tried on glasses with different frames and lenses. polarized lenses regular lenses cat eye frames 3 3 browline frames 5 8 what is the probability that a randomly selected pair of sunglasses has browline frames given that the pair of sunglasses has polarized lenses? simplify any fractions.
Answer
Explanation:
Step1: Find number of polarized - lens sunglasses
The number of sunglasses with polarized lenses is the sum of cat - eye frames with polarized lenses and browline frames with polarized lenses. So, $3 + 5=8$.
Step2: Find number of polarized - lens sunglasses with browline frames
The number of sunglasses with polarized lenses and browline frames is 5.
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 having browline frames and $B$ is the event of having polarized lenses, then $P(A|B)=\frac{n(A\cap B)}{n(B)}$. Here, $n(A\cap B) = 5$ and $n(B)=8$. So the probability is $\frac{5}{8}$.
Answer:
$\frac{5}{8}$