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(1|b)=

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 contingency table, if \(A\) represents Group 1 and \(B\) represents Project B, then \(P(1|B)=\frac{\text{Number of elements in Group 1 and Project B}}{\text{Total number of elements in Project B}}\).

Step2: Identify the relevant values from the table

From the table, the number of elements in Group 1 and Project B is \(6\), and the total number of elements in Project B is \(16\).

Step3: Calculate the probability

Substitute the values into the formula: \(P(1|B)=\frac{6}{16}=\frac{3}{8} = 0.375\).

Answer:

\(0.375\)