Question

If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fail is.

• A. 0.38
• B. 0.44
• C. 0.50
• D. 0.94

Hint:

To calculate the probability that either of two independent events occurs, use the formula for the union of two events.

Answer 1

The Correct Option is B

Let \( P(A) = 0.2 \) and \( P(B) = 0.3 \). We are asked to find the probability that either A or B fail. This can be expressed as \( P(A \cup B) \). Using the formula for the union of two events: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Since the events A and B are independent, we have: \[ P(A \cap B) = P(A) \times P(B) = 0.2 \times 0.3 = 0.06 \] Now, substitute the values into the formula: \[ P(A \cup B) = 0.2 + 0.3 - 0.06 = 0.44 \] Thus, the correct answer is (B) 0.44.