Question

In a town, the probability that a person attends a gym on weekdays is 0.7, the probability that a person attends the gym on weekends is 0.4, and the probability that a person attends the gym on weekdays or weekends, or both is 0.3. What is the probability that a person attends the gym on both weekdays and weekends?

• A. 0.6
• B. 0.7
• C. 0.8
• D. 0.9

Hint:

Use the formula \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \) to find intersection probabilities in overlapping events.

Answer 1

The Correct Option is C

Let \( A \) be the event "person attends gym on weekdays" and \( B \) be "attends gym on weekends". We are given: \[ P(A) = 0.7, \quad P(B) = 0.4, \quad P(A \cup B) = 0.3 \] Using the identity: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Substitute values: \[ 0.3 = 0.7 + 0.4 - P(A \cap B) \Rightarrow P(A \cap B) = 1.1 - 0.3 = 0.8 \]