3. Max has a gambling problem. One day, he buys eleven scratch cards at one time (a scratch card is a type of lottery ticket). Each card is a winning ticket with probability 0.25. Since the total number of issued tickets is very large, you may assume that the probability of a win for each ticket is independent of the other tickets. a) Find the probability that at least four of the eleven scratch cards are winning tickets. Choose the alternative closest to your answer. (5p) (A) 0.034 (B) 0.050 (C) 0.11 (D) 0.17 (E) 0.29 Serhiy and William run a 200 meter race. Assume that Serhiy's race time is normally distributed with mean 25 seconds and standard deviation 1.5 seconds. Assume that William's race time is normally distributed with mean 26 seconds and standard deviation 2 seconds. During this race, the correlation between the two race times is 0.2. b) Find the probability that Serhiy wins the race against William. Choose the alternative closest to your answer. (5p) (A) 0.33 (B) 0.42 (C) 0.58 (D) 0.67 (E) 0.75