The Powerball lottery is open to participants across several states. When enteri

Question

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, whatâAZs 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 = 59C5 * 35= 59!/(54!*5!)* 35= 175223510

Odds are thus 1 in 175223510

b) 1 million - Number of ways = 59!/(54!*5!) =5006386*35/34 = 5153632

Odds are thus 1 in 5153632

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