If A and B are two events such that P (A \cup B) = 5/6, P(A) = 1/4, P(B) = 1/3, then A and B are

Correct Answer is : independent

Probability Practice Test 1

Question : 15 of 40

Marks: +1, -0

If A and B are two events such that

P (A ∪ B) = 5/6

P(A) = 1/4

P(B) = 1/3

, then A and B are

Solution:

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
∴ P(A ∩ B)

= 1/3 + 3/4 – 5/6 = 3/12 = 1/4

P(A) P(B)

= 1/3 . 3/4 = 1/4

As P(A) P(B) = P(A ∩ B)
∴ A and B are independent.
Also P(A ∩ B) ≠ 0
∴ A and B are not exclusive.

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