Question

If \( A \) and \( B \) are independent events, where \( P(A) = \frac{3{10} \), \( P(B) = \frac{6}{10} \), then find \( P(A \cup B) \) and \( P(A \cap B) \).}

Hint:

For independent events, \( P(A \cap B) = P(A) \times P(B) \) and \( P(A \cup B) \) follows the formula \( P(A) + P(B) - P(A \cap B) \).

Answer 1

Using the formula for independent events: \[ P(A \cap B) = P(A) \times P(B), \] \[ P(A \cup B) = P(A) + P(B) - P(A \cap B). \] Substituting the values: \[ P(A \cap B) = \frac{3}{10} \times \frac{6}{10} = \frac{18}{100} = \frac{9}{50}. \] \[ P(A \cup B) = \frac{3}{10} + \frac{6}{10} - \frac{9}{50} = \frac{15}{25} - \frac{9}{50} = \frac{21}{25}. \]