cassie was the lucky journalist assigned to cover the best beard competition. she recorded the contestants…

cassie was the lucky journalist assigned to cover the best beard competition. she recorded the contestants beard colors in her notepad. cassie also noted if the contestants were signed up for the mustache competition later in the day.\n| |only in the beard competition|also in the mustache competition|\n|--|--|--|\n|red beard|3|1|\n|grey beard|2|5|\nwhat is the probability that a randomly selected contestant is also in the mustache competition given that the contestant has a grey beard?\nsimplify any fractions.

cassie was the lucky journalist assigned to cover the best beard competition. she recorded the contestants beard colors in her notepad. cassie also noted if the contestants were signed up for the mustache competition later in the day.\n| |only in the beard competition|also in the mustache competition|\n|--|--|--|\n|red beard|3|1|\n|grey beard|2|5|\nwhat is the probability that a randomly selected contestant is also in the mustache competition given that the contestant has a grey beard?\nsimplify any fractions.

Answer

Explanation:

Step1: Calculate total grey - bearded contestants

The number of grey - bearded contestants is the sum of those only in the beard competition and those also in the mustache competition. So, $2 + 5=7$.

Step2: Calculate number of grey - bearded contestants in mustache competition

The number of grey - bearded contestants also in the mustache competition is 5.

Step3: Calculate the conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In this case, the probability that a contestant is in the mustache competition given they have a grey beard is the number of grey - bearded contestants in the mustache competition divided by the total number of grey - bearded contestants. So the probability is $\frac{5}{7}$.

Answer:

$\frac{5}{7}$