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).
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).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Transcribed Image Text: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).
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.)
b. What is the probability that a $2 lottery ticket wins the Powerball lottery?
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