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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
Options
> 0.5
0.5
≤ 0.5
0
Solution
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
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