If P(A) = 6/11 , P(B) = 5/11 and P(A ∪ B) = 7/11, find
(i) P(A∩B) (ii) P(A|B) (iii) P(B|A)

Question

If P(A) = 6/11 , P(B) = 5/11 and P(A ∪ B) = 7/11, find (i) P(A ∩ B) (ii) P(A|B) (iii) P(B|A)

Philoid · Accepted Answer

Given:

(i) We know that P(A * B) = P(A) + P(B) – P(A ∩ B)

⇒ P(A ∩ B) = P(A) + P(B) – P(A ∪ B)

(ii) Now, ∵ By definition of conditional probability,

(iii) Again, ∵ By definition of conditional probability,

If P(A) = 6/11 , P(B) = 5/11 and P(A ∪ B) = 7/11, find(i) P(A∩B) (ii) P(A|B) (iii) P(B|A)