The Massachusetts state lottery game, Cash WinFall, used to have a way that anyone with enough money and time could stand a good chance of getting rich, and it is reported that an MIT computer scientist did just that. In this game, a player picks 6 numbers from the range from 1 to 46. If he matches all 6, then he could win as much as $2 million, but the odds of that payout don’t justify a bet, so let us ignore the possibility of winning this jackpot. Nevertheless, there were times when matching just 5 of the 6 numbers in a $2 lottery ticket would pay $100,000. Suppose in this scenario that you were able to bet $600,000. 

(a) What is the expected amount that you would win? 

(b) Derive a bound on the probability that you would lose $300,000 or more in this scenario, that is, that you would have 3 or fewer of the 5 of the 6 winning tickets.