Powerball! Imagine, you could win a jackpot worth at least 40million. Some jackpots have been worth more than 250million! Powerball is a multistate lottery. To play Powerball, you purchase a $2ticket. On the ticket you select five distinct white balls (numbered 1through69)and then one red Powerball (numbered 1through 26). The red Powerball number may be any of the numbers 1through 26,including any such numbers you selected for the white balls. Every Wednesday and Saturday there is a drawing. If your chosen numbers match those drawn, you win!Figure 6-7shows all the prizes and the probability of winning each prize and specifies how many numbers on your ticket must match those drawn to win the prize.

(a) Assume the jackpot is 40millionand there will be only one jackpot winner.Figure 6-7lists the prizes and the probability of winning each prize. What is the probability ofnot winningany prize?

Consider all the prizes and their respective probabilities, and the prize of $0 (no win) and its probability. Use all these values to estimate your expected winnings ifyou play one ticket. How much do you effectively contribute to the state in which you purchased the ticket (ignoring the overhead cost of operating Powerball)?

(b) Suppose the jackpot increased to 100million(and there was to be only one winner). Compute your expected winnings if you buy one ticket. Does the probability of winning the jackpot change because the jackpot is higher?

(c) The probability of winninganyprize is about 0.0402.Suppose you decide to buy five tickets. Use the binomial distribution to compute the probability of winning (any prize) at least once.Note:You will need to use the binomial formula. Carry at least three digits after the decimal.