For any two independent events A and B, P(A - B) is equal to:

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SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )
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  1. P(A) - P(A)P(B)
  2. P(B) - P(A)
  3. P(B) (1 - P(AB))
  4. P(A) - P(B)

Answer (Detailed Solution Below)

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

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Given:

Two independent events A and B

Formula Used:

P(A - B) = P(A) - P(A ∩ B)

For independent events, P(A ∩ B) = P(A) × P(B)

Calculation:

We need to find P(A - B).

P(A - B) = P(A) - P(A ∩ B)

Since A and B are independent events:

P(A ∩ B) = P(A) × P(B)

Therefore, P(A - B) = P(A) - P(A) × P(B)

Solution:

P(A - B) = P(A) - P(A) × P(B)

P(A - B) = P(A)(1 - P(B))

Therefore, P(A - B) = P(A)(1 - P(B)).

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