​ If A and B are events such that P(A) = 1/2, P(B) = 7/12 and P(A' ∪ B') = 1/4 then A and B are A. Independent

Question

If A and B are events such that P(A) = \(\frac{1}{2},\) P(B) = \(\frac{7}{12}\) and P(A' ∪ B') = \(\frac{1}{4},\) then A and B are

A. Independent

B. Mutually exclusive

C. Both ‘a’ and ‘b.’

D. None of these

Answer 1

Correct answer is D.

We are having two events A and B such that

\(\Rightarrow\) As P(A ∩ B) ≠ P(A).P(B) … thus, they are not independent,

\(\Rightarrow\) And as P(A ∪ B) ≠ P(A) + P(B) … thus, they are not mutually exclusive.