If the probability for A to fail in an examination is 0.2 and that for

1.	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 isA. > 0.5B. 0.5C. ≤ 0.5D. 0
Answer» 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.

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 isA. > 0.5B. 0.5C. ≤ 0.5D. 0

Answer»

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.

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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 isA. &gt; 0.5B. 0.5C. ≤ 0.5D. 0

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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 isA. > 0.5B. 0.5C. ≤ 0.5D. 0