Question 5-9

5. A and B are two events such that P(A)= 0.4, P((B|A)= 0.7, and P(A' n B)=0.3. Find: a) P(An B) b) P(B) c) P(A UB) d) P(A|B) 6. If A and B are two events and P(B) = 2 , P(An B) = , and P(BIA)= 2. Find: a) P(A) b) P(A|B) c) P(A|B') d) State with reasons, whether A and B are: I. Independent II. Mutually exclusive 7. A and B are two events such that P(A)= 0.5 and P(B)= 0.2 and P(AUB) = 0.6. a) Determine: I. P(An B) II. P(An B') III. P(A'n B) IV. P(A'n B' ) V . P(A U B') 8. A sample space contains the events A and B satisfying P(A)= -, P(B) = -, P(AnB') = a) Find P(A n B) b) Are A and B independent? c) Find P(A'|B) 9. In an annual club election, there are three possible candidates. The probability of Mr. Mawi, Mr. Yazer and Mr. Jefri being nominated are 0.15, 0.55 and 0.30 respectively. If the nominated candidates take part in the election, the probabilities that the election is won by Mr. Mawi, Mr. Yazer and Mr. Jefri are 0.50, 0.65 and 0.4 respectively. a) Draw a tree diagram for the above information. b) Given that someone won the election, what is the probability that the winner is Mr. Mawi