Question

project a project b project c total group 1 7 9 5 21 group 2 9 11 9 29 total 16 20 14 50 p(a|1)=

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, \( P(A|1) \) (probability of project A given group 1) can be calculated as \( \frac{\text{Number of Group 1 in Project A}}{\text{Total of Group 1}} \).

Step2: Substitute the values from the table

From the table, the number of Group 1 in Project A is \( 7 \), and the total of Group 1 is \( 21 \). So \( P(A|1)=\frac{7}{21} \).

Step3: Simplify the fraction

Simplify \( \frac{7}{21} \) by dividing numerator and denominator by \( 7 \). \( \frac{7\div7}{21\div7}=\frac{1}{3} \).

Answer:

\(\frac{1}{3}\)