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\n| | only in the beard competition | also in the mustache competition |\n| :--- | :---: | :---: |\n| red beard | 3 | 1 |\n| grey beard | 2 | 5 |\n\nwhat is the probability that a randomly selected contestant is also in the mustache competition given that the contestant has a grey beard?\n\nsimplify any fractions.
Answer
Explanation:
Step1: Identify the total number of grey beards
$$2 + 5 = 7$$
Step2: Identify grey beards in mustache competition
$$5$$
Step3: Calculate the conditional probability
$$P(\text{Mustache} | \text{Grey}) = \frac{\text{Grey and Mustache}}{\text{Total Grey}}$$
Step4: Substitute the values into the formula
$$\frac{5}{7}$$
Answer:
$\frac{5}{7}$