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If the probabilities 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

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If the probabilities 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. > . 5 B. .5 C. ≤ .5 D. 0 Select the correct answer from above options

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Let E1 be the event that A fails in an examination and E2 be the event that B fails in an examination Then, we have P (E1) = 0.2 and P (E2) = 0.3 Now, we have to find the P (either E1 or E2 fails) ∴ P(either E1 or E2 fails) = P(E1) + P(E2) – P(E1⋂ E2) ≤ P(E1) + P(E2) ≤ 0.2 + 0.3 ≤ 0.5 Hence, the correct option is (C)

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