If A and B are two events such that P(A ∪ B) = 3/4 , P(A ∩ B)= 1/4 and P(B) = 1/2 then the events A and B are ___

If A and B are two events such that P(A ∪ B) = 3/4 , P(A ∩…

If A and B are two events such that P(A ∪ B) = $\frac 3 4$ , P(A ∩ B)= $\frac 1 4$ and P(B) = $\frac 1 2$ then the events A and B are ___________

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Correct answer: B

Explanation

The correct answer is option 2 i.e. Independent.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

⇒ 3/4 = P(A) + 1/2 - 1/4

⇒ 3/4 = P(A) + 1/4

⇒ P(A) = 3/4 - 1/4 = 1/2

Two events A and B are independent if P(A ∩ B) = P(A) × P(B)

P(A) × P(B) = (1/2) × (1/2) = 1/4

Since P(A ∩ B) = 1/4, which is equal to P(A) × P(B)

Therefore, the events A and B are independent.