Question

project a project b project c total
group 1 5 6 4 15
group 2 9 10 6 25
total 14 16 14 44
p(a|2)=

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \( P(A|B)=\frac{P(A\cap B)}{P(B)} \). In the context of a two - way table, if \( A \) is the event of being in Project \( A \) and \( B \) is the event of being in Group \( 2 \), then \( P(A|2)=\frac{\text{Number of people in Group 2 and Project A}}{\text{Number of people in Group 2}} \).

Step2: Identify the values from the table

From the table, the number of people in Group 2 and Project A is \( 9 \), and the number of people in Group 2 is \( 25 \).

Answer:

\(\frac{9}{25}\)