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…

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 ( A ) be "working on Project A" and ( B ) be "working in Group 1". So ( P(1|A) = \frac{P(1 \cap A)}{P(A)} ).

Step2: Find ( P(1 \cap A) ) and ( P(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(1 \cap A) = \frac{5}{21} ). The number of people in Project A is 12, so ( P(A) = \frac{12}{21} ).

Step3: Calculate ( P(1|A) )

Substitute into the formula: ( P(1|A) = \frac{\frac{5}{21}}{\frac{12}{21}} = \frac{5}{12} ).

Answer:

(\frac{5}{12})