Question

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

	freshman	sophomore	junior	senior
girl	5	5	4	2

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

Explanation:

Step1: Calculate P(A and B)

The number of junior - boy students is 7. The total number of students is \(7 + 9+7 + 5+5 + 5+4 + 2=44\). So \(P(A\text{ and }B)=\frac{7}{44}\)

Step2: Calculate P(A)

The number of junior students is \(7 + 4=11\). So \(P(A)=\frac{11}{44}\)

Step3: Calculate P(B|A)

Using the formula \(P(B|A)=\frac{P(A\text{ and }B)}{P(A)}\), we substitute the values: \(P(B|A)=\frac{\frac{7}{44}}{\frac{11}{44}}=\frac{7}{11}\)

Answer:

\(\frac{7}{11}\)