The Powerball lottery is played twice each week in 31 states, the District of Co

Question

The Powerball lottery is played twice each week in 31 states, the District of Columbia, and the Virgin Islands. To play Powerball. a participant must purchase a $ 2 ticket, select five numbers from the digits 1 through 59. and then select a Powerball number from the digits 1 through 35. To determine the winning numbers for each game, lottery officials draw 5 white balls out a drum of 59 white balls numbered 1 through 59 and 1 red ball out of a drum of 35 red balls numbered 1 through 35. To win the Powerball jackpot, a participant s numbers must match the numbers on the 5 white balls in any order and must also match the number on the red Powerball. The numbers 5-16-22-23-29 with a Powerball number of 6 provided the record jackpot of $ 580 million (Powerball website. November 29.2012). How many Powerball lottery outcomes are possible? What is the probability that a $ 2 lottery ticket wins the Powerball lottery?

Explanation / Answer

A) Number of possible outcomes = Number of outcomes on whiteballs x number of outcomes on red ball

= 59C5 x 35

= [59!/((5!)x(59-5)!)]x35

= 175,223,510

B) P($2 ticket winning the powerball lottery) = 1/175,223,510 = 5.7x10-9

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