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
boy: freshman 7, sophomore 9, junior 7, senior 5
girl: freshman 5, sophomore 5, junior 4, senior 2
p(senior|boy)=\frac{?}{}
p(b|a)=\frac{p(a and b)}{p(a)}

Explanation:

Step1: Calculate the total number of boys

Add the number of boys in each grade: \(7 + 9+7 + 5=28\)

Step2: Identify the number of senior - boy

From the table, the number of senior - boy is \(5\)

Step3: Apply the conditional - probability formula

The formula for conditional probability \(P(\text{Senior}|\text{Boy})=\frac{\text{Number of senior - boys}}{\text{Total number of boys}}\)
Substitute the values: \(P(\text{Senior}|\text{Boy})=\frac{5}{28}\)

Answer:

\(\frac{5}{28}\)