Question

1. a student is chosen at random. if the probability that the student is taking math this semester is 37/50, the probability that the student is on the soccer team is 2/125, and the probability that the student is doing both is 4/305, determine p(taking math|on the soccer team).

a 81.97%
b 61.78%
c 46.25%
d 5.24%

Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(A|B) = \frac{P(A \cap B)}{P(B)} \), where \( A \) is "taking math" and \( B \) is "on the soccer team".

Step2: Identify Given Probabilities

We know \( P(A \cap B) = \frac{4}{305} \) and \( P(B) = \frac{2}{125} \).

Step3: Substitute into Formula

\( P(\text{taking math}|\text{on the soccer team}) = \frac{\frac{4}{305}}{\frac{2}{125}} \)
Simplify the division of fractions: \( \frac{4}{305} \times \frac{125}{2} = \frac{4 \times 125}{305 \times 2} = \frac{500}{610} \approx 0.8197 \)
Convert to percentage: \( 0.8197 \times 100 \approx 81.97\% \)

Answer:

A. 81.97%