Find the probability of occurrence of at least one of A and B, If A and B are two independent events?

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AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 1)
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  1. 1- P(A’) P(B’)
  2. 1+ P(A’) P(B’)
  3. P(A’) - P(B’) - 1
  4. P(A’) - P(B’) + 1

Answer (Detailed Solution Below)

Option 1 : 1- P(A’) P(B’)
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Detailed Solution

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Given:

A and B are two independent events.

Concept:

For any two independent events A and B : P(A ∩ B) = P(A)·P(B)

Explanation:

The probability of occurrence of at least one of A and B means " A but not B or B but not A or A and B both ".

Indirectly it means '1 - probability of occurrence of neither A and B'.

⇒ P(at least one of A and B) = 1 - P(neither A and B)

⇒ P(at least one of A and B) = 1 - P(A' ∩ B')

Now, P(A' ∩ B') = P(A’) P(B’) as A and B are independent events.

⇒ P(at least one of A and B) = 1 - P(A')P(B')

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