The probability that John passes the Mathematics course is 0.55 and the probability that he passes the English course is 0.72. The probability that he passes the Mathematics course. given that he passes the English course. is 0.63. Find: (a) the probability that John passes both the courses. (b) the probability that John passes at least one of the courses. (c) the probability that John [ailsthe English course given that he passes the Mathematics course. (7 marks) The event A and B are such that P(A)=x+0.2 . P(B)=2.r+0.l and P(AnB)=x (a) Given that Pp! U3) = 0.7 . nd (i) 1. (ii) P(Zn). (ii) P(A|B) . (4 marks) (b) Are the events A and 8 independent? Explain briey. [2 marks) (C) Are the events A and B mutually exclusive? Explain briey? [2 marks)