SOLUTION: 6. The Powerball lottery is played twice each week in 28 states, the Virgin Islands, and the District of Columbia. To play Powerball a participant must purchase a ticket and then

Question 1165737: 6. The Powerball lottery is played twice each week in 28 states, the Virgin Islands, and the
District of Columbia. To play Powerball a participant must purchase a ticket and then select
five numbers from the digits 1 through 55 and a Powerball number from the digits 1 through
42. To determine the winning numbers for each game, lottery officials draw five white balls
out of a drum with 55 white balls, and one red ball out of a drum with 42 red balls. To win
the jackpot, a participant’s numbers must match the numbers on the five white balls in any
order and the number on the red Powerball. Eight coworkers at the ConAgra Foods plant
in Lincoln, Nebraska, claimed the record $365 million jackpot on February 18, 2006, by
matching the numbers 15-17-43-44-49 and the Powerball number 29. A variety of other
cash prizes are awarded each time the game is played. For instance, a prize of $200,000
is paid if the participant’s five numbers match the numbers on the five white balls
(www.powerball.com, March 19, 2006).
a. Compute the number of ways the first five numbers can be selected.
b. What is the probability of winning a prize of $200,000 by matching the numbers on
the five white balls?
c. What is the probability of winning the Powerball jackpot?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
a. It is 55*54*53*52*51=417,451,320
b.(5/55)(4/54)(3/53)(2/52)(1/51)=0.000000287 (or 2.87 x 10^(-7)) or 1 in 3,478,761
for winning the jackpot, it is the above probability *1/42, the probability of drawing the red Powerball.
c. this is 0.000000006844 (6.8 x 10^(-9)) or 1 in 146,107,962

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