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)
(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,
An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?