Please show work! 16. Probability and Lotteries The Powerball lottery is open to
ID: 3044907 • Letter: P
Question
Please show work!
16. Probability and Lotteries The Powerball lottery is open to participants across several states. When entering the powerball lottery, a participant selects five numbers from 1-59 and then selects a powerball number from the digits 1-35. In addition, there's a $1 million payoff for anybody selecting the first five numbers correctly » Show that the odds of winning the Powerball Jackpot are 1 in 175, 223, 510. Show that the odds of winning the $1 million are 1 in 5, 153, 632 On February 18, 2006 the Jackpot reached $365 million. Assuming that you will either win the Jackpot or the $1 million prize, whatâA2s your expected value of winning? Mega Millions is a similar lottery where you pick 5 balls out of 56 and a powerball from 46. Show that the odds of winning mega millions are higher than the Powerball lottery On March 30, 2012 the Jackpot reached $656 million. Is your expected value higher or lower than that calculated for the Powerball lottery?Explanation / Answer
number of ways of winning power ball = 59C5*35= 175223510
Number of ways of winning 1 million = 59C5 * 35/34= 5153632
Expected value of wiining = 365 * 10^6 /175223510 + 10^6/5153632= 2.27 dollars
Odds in mega millions = 56C5 * 46 = 56!/[51!*5!]*46=175711536
Number of ways of winning 1 million =56!/[51!*5!]*46/45= 3904700
Expected winnings= [656/175711536 +1/3904700]*10^6=3.989 dollars