Question

The probabilities of occurrences of two independent events \( A \) and \( B \) are 0.5 and 0.8, respectively. What is the probability of occurrence of at least \( A \) or \( B \) (rounded off to one decimal place)?

Hint:

To calculate the probability of "at least" one event happening, use the formula for the union of events. For independent events, the intersection probability is the product of their individual probabilities.

Answer 1

The probability of occurrence of at least \( A \) or \( B \) is given by the formula for the union of two independent events: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Since \( A \) and \( B \) are independent events, the probability of both occurring simultaneously is: \[ P(A \cap B) = P(A) \times P(B) \] Substitute the given values: \[ P(A) = 0.5, P(B) = 0.8 \] Thus, \[ P(A \cup B) = 0.5 + 0.8 - (0.5 \times 0.8) = 0.5 + 0.8 - 0.4 = 0.9 \] \[ \boxed{P(A \cup B) = 0.9} \]