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
Let A be the event that student ‘A’ fails in exam and B be the event that student ‘B’ fails in exam.
Given, P(A) = 0.2 and P(B) = 0.3
We have to find P(A ∪ B)
We know that P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
As P(A ∩ B) not given, but we know that – 0 ≤ P(A ∩ B) ≤ 1
∴ P(A ∪ B) = 0.2 + 0.3 – P(A ∩ B) = 0.5 - P(A ∩ B)
Clearly a +ve number will be subtracted form 0.5 to make it equal to P(A ∪ B).
∴ P(A ∪ B) ≤ 0.5
As our answer matches with option (c)
∴ Option (c) is the only correct choice.