Question

a student is randomly selected from this table. what is the probability that they are a senior, given that they are a boy?
students on a team

	freshman	sophomore	junior	senior
girl	5	5	4	2

p(senior|boy) =
p(b|a) = \frac{p(a and b)}{p(a)}

Explanation:

Step1: Find number of boys

Add up number of boys in each grade level. $7 + 9+7 + 5=28$.

Step2: Find number of senior - boys

Number of senior - boys is 5.

Step3: Calculate conditional probability

$P(\text{Senior}|\text{Boy})=\frac{\text{Number of senior - boys}}{\text{Number of boys}}=\frac{5}{28}$.

Answer:

$\frac{5}{28}$