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 fails is:

• A. \( \leq 0.4 \)
• B. \( \leq 0.25 \)
• C. \( \leq 0.5 \)
• D. \( \leq 0.7 \)

Hint:

To find the probability of the union of two events, use the formula \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \), and adjust for the dependence or independence of the events.

Answer 1

The Correct Option is C

Let the probability that A fails be \( P(A) = 0.2 \), and the probability that B fails be \( P(B) = 0.3 \). The probability that either A or B fails is the probability of the union of two events,
given by:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B). \] Assuming A and B are independent events, the probability of both A and B failing is: \[ P(A \cap B) = P(A) \times P(B) = 0.2 \times 0.3 = 0.06. \] Thus, the probability that either A or B fails is: \[ P(A \cup B) = 0.2 + 0.3 - 0.06 = 0.44. \] Therefore, the correct answer is \( 0.44 \), which is less than or equal to 0.5.