Question

Find \( P(G \cap \overline{H}) \), where \( G \) is the event of Jaspreet's selection and \( \overline{H} \) denotes the event that Rohit is not selected.

Hint:

For independent events, the probability of their intersection is the product of their individual probabilities.

Answer 1

Step 1: Compute the probability
The probability \( P(G \cap \overline{H}) \) is given by: \[ P(G \cap \overline{H}) = P(G) \cdot P(\overline{H}), \] where \( P(G) = \frac{1}{3} \) and \( P(\overline{H}) = 1 - P(H) = 1 - \frac{1}{5} = \frac{4}{5} \). \[ P(G \cap \overline{H}) = \frac{1}{3} \cdot \frac{4}{5} = \frac{4}{15}. \] Final Result: The probability \( P(G \cap \overline{H}) \) is \( \frac{4}{15} \).