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(2|c)=

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, \( P(2|C)=\frac{\text{Number of Group 2 in Project C}}{\text{Total number in Project C}} \).

Step2: Identify the relevant values from the table

From the table, the number of Group 2 in Project C is \( 6 \), and the total number in Project C is \( 14 \).

Step3: Calculate the probability

Substitute the values into the formula: \( P(2|C)=\frac{6}{14}=\frac{3}{7}\approx0.4286 \).

Answer:

\( \frac{3}{7} \)