Question

project a project b total group 1 5 6 11 group 2 7 3 10 total 12 9 21 what is the probability of working in group 1, if working on project a? p(1|a)=

Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(B|A) = \frac{P(A \cap B)}{P(A)} \). In this case, let \( B \) be "Group 1" and \( A \) be "Project A". So \( P(1|A) = \frac{P(\text{Group 1 and Project A})}{P(\text{Project A})} \).

Step2: Find \( P(\text{Group 1 and Project A}) \) and \( P(\text{Project A}) \)

From the table, the number of people in Group 1 and Project A is 5, and the total number of people is 21. So \( P(\text{Group 1 and Project A}) = \frac{5}{21} \). The number of people in Project A is 12, so \( P(\text{Project A}) = \frac{12}{21} \).

Step3: Apply the Formula

Substitute into the conditional probability formula: \( P(1|A) = \frac{\frac{5}{21}}{\frac{12}{21}} \). The 21 in the numerator and denominator cancels out, giving \( \frac{5}{12} \).

Answer:

\(\frac{5}{12}\)