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) > 0.5 (b) 0.5 (c) ≤ 0.5 (d) 0

Answer 1

Let X and Y be two events given by

X : A fails in an examination

Y : B fails in an examination

P(A fails) = P(X) = 0.2

P(B fails) = P(Y) = 0.3

Now, P(either A or B fails) = P(X ∪ Y)

We know that,

P(X ∪ Y) ≤ P(X) + P(Y) = 0.2 + 0.3 = 0.5

⇒ P(X ∪ Y) ≤ 0.5

∴ P(either A or B fails) ≤ 0.5

Hence, the correct answer is option (c).