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|1)=

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 the table, \( P(A|1) \) (probability of project A given group 1) can be calculated as \( \frac{\text{Number of people in group 1 working on project A}}{\text{Total number of people in group 1}} \).

Step2: Identify the values from the table

From the table, the number of people in group 1 working on project A is \( 5 \), and the total number of people in group 1 is \( 15 \).

Step3: Calculate the probability

Substitute the values into the formula: \( P(A|1)=\frac{5}{15}=\frac{1}{3}\approx0.333 \).

Answer:

\(\frac{1}{3}\)