The Powerball lottery is played twice each week in 31 states, the District of Columbia, andthe Virgin Islands. To play Powerball, a participant must purchase a $2 ticket, select fivenumbers from the digits 1 through 59, and then select a Powerball number from the digits 1through 35. To determine the winning numbers for each game, lottery officials draw 5white balls out a drum of 59 white balls numbered 1 through 59 and 1 red ball out of adrum of 35 red balls numbered 1 through 35. To win the Powerball jackpot, a participant’snumbers must match the numbers on the 5 white balls in any order and must also matchthe number on the red Powerball. The numbers 5–16–22–23–29 with a Powerball numberof 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-steprandom experiment. Select the 5 white ball numbers and then select the 1 red Powerballnumber.)b. What is the probability that a $2 lottery ticket wins the Powerball lottery?
Permutations and Combinations
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.
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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