Question

(a) The chances that an academician, a business man and a politician becoming Vice Chancellor of a university are 0.5, 0.3 and 0.2 respectively. The probability that research work will be promoted in the university by these 3 gentlemen are respectively are 0.8, 0.6 and 0.4. It is found research work has been promoted by the university. What is the chance that an academician has become the VC?

(b) A can hit a target 3 times in 5 shots; B can hit 2 times in 5 shots; C can hit 3 times in 4 shots. They fire a volley. What is the probability that two shots hit?