4. Despite warnings of your statistics professor, you decide to gamble every month in two inde- pendent lotteries. Your strategy is to stop playing as soon as you win a prize of at least $1 million in at least one of the two lotteries. Suppose that every time you play in these two lotteries, the probabilities of winning $1 million are 301 and 332, respectively. Let T be the number of times you play until winning at least one prize. (a) What is the distribution of T and what is/ are its parameter(s)? (b) What is the expected numer of times you need to play until you win at least one prize? (0) Suppose p1 = 1 /292, 201,338 (US Powerball) and p2 = 1/302,575, 350 (US Mega Mil- lions). If lottery tickets for both lotteries cost $10, what is the expected pay-off of your gambling strategy? (Hint: Use your answer to part (b). Also: You will realize that you will not want to actually implement your gambling strategy.)