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|a)=

Explanation:

Step1: Recall the formula for conditional probability

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

Step2: Identify the relevant values from the table

From the table, the number of elements in Group 2 and Project A is \(9\), and the total number of elements in Project A is \(14\).

Step3: Calculate the probability

Substitute the values into the formula: \(P(2|A)=\frac{9}{14}\approx0.643\).

Answer:

\(\frac{9}{14}\)