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.

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:

$\frac{5}{8}$