Chapter 4.1, Problem 12E

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).

1. a. How many Powerball lottery outcomes are possible? (Hint: Consider this a two-step random experiment. Select the 5 white ball numbers and then select the 1 red Powerball number.)
2. b. What is the probability that a $2 lottery ticket wins the Powerball lottery?