12. The Powerball lottery is played twice each week in 31 states, the District o
ID: 3306702 • Letter: 1
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12. The Powerball lottery is played twice each week in 31 states, the District of Columbia, and the Virgin Islands. To play Powerbal, 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 five white balls out a drum of 59 white balls numbered 1 through 59 and one 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 five 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). a. How many Powerball lottery outcomes are possible? (Hint: Consider this a two-step 2 experiment. Select the five white ball numbers and then select the one red Powerball number.) b. What is the probability that a $2 lottery ticket wins the Powerbal lottery?Explanation / Answer
Solution:-) Draw 5 balls out of 59 white balls. So,the number of possible outcomes is 59C5 =(59 x 58 x 57 x 56 x 55) / (5 x 4 x 3 x 2 x 1) = 5006386
In addition to match the first 5, you must also match the one red Powerball. as the red powerballs are 35, So there are 35 ways to choose one red powerball.
So, the total number of powerballs lottery outcomes are =5006386 x 35 = 175223510.
b) In addition to match the first 5, you must also match the Powerball.
P(match 5 and powerball) = 1/(5006386) x 1/(35)
= 1 / 175223510..
The probability that $2 lottery ticket wins the probability is 1 / 175223510...
CHEERS!!
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