Correct Answer - Option 3 : 0.875
Concept:
For any tow independent events A and B, if P(A) and P(B) are their probability of occurring then:
- P(A ∩ B) = P(A) × P(B)
- P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
- P(A') = 1 - P(A)
- P(B') = 1 - P(B)
Calculation:
Given P(B') = 0.32 and P(A∪B) = 0.72
Now P(B') = 1 - P(B)
⇒ P(B) = 1 - 0.32 = 0.68
Let P(A) = x
∵ P(A ∩ B) = P(A) × P(B)
⇒ P(A ∩ B) = 0.68 x
As P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
⇒ 0.72 = x + 0.68 - 0.68 x
⇒ 0.04 = 0.32 x
⇒ x = 0.125
∴ P(A) = 0.125
P(A') = 1 - P(A)
P(A') = 1 - 0.125
P(A') = 0.875
