Question 2 John is goes to the casino and plays a slot machine. The probability that he wins on the first spin For all subsequent spins, the probability of John winning will be if John wins in the 5 preceding round, and the probability of John winning will be preceding round. 15 if John did not win in the (a) John plays 3 rounds. Find the probability that he wins on the third round, given that he only won two rounds of the three. (b) (4 marks) Let X denote the number of rounds John need to play before he finally wins for the first time. Comment on the suitability of modelling X after the geometric distribution. Compute P(X = 5). (c) (3 marks) John visits the casino on 20 separate days, he played exactly 10 rounds on each day. Let Y denote the number of days (out of 20) that John does not win anything. State any necessary assumptions required in order to suitably model Y after the binomial distribution. State clearly the parameters of this binomial distribution as well. (4 marks) (d) Assume that your assumptions in Question 2(c) hold. Compute E(Y) and Var(Y). (4 marks)