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.\n| |polarized lenses|regular lenses|\n|--|--|--|--|\n|cat eye frames|3|3|\n|browline frames|5|8|\nwhat is the probability that a randomly selected pair of sunglasses has browline frames given that the pair of sunglasses has polarized lenses?\nsimplify 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.\n| |polarized lenses|regular lenses|\n|--|--|--|--|\n|cat eye frames|3|3|\n|browline frames|5|8|\nwhat is the probability that a randomly selected pair of sunglasses has browline frames given that the pair of sunglasses has polarized lenses?\nsimplify 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: Calculate conditional probability

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:

$\frac{5}{8}$