The expected winnings are defined as the value of the jackpot multiplied by the probability of winning it. How large should the Powerball jackpot be in order for the expected winnings to exceed the ticket price ($2)?
The Powerball lottery drawing of January 13th, 2016 had the largest payoff in its history, of $1.6 billion dollars. The lottery draw consists of picking 5 white balls at random, from an urn of 69 balls, numbered from 1 to 69 (without replacement, and the order of the balls is not important). In addition, a “powerball” is picked at random from an urn of 26 red balls, numbered 1 through 26. For a $2 ticket you can choose the 5 winning white balls and the winning “powerball”. In this problem we will study the probability of winning this lottery. Assume that you purchase a $2 ticket.
5 balls can picked up without replacement from the urn of 69 balls in 69 * 68 * 67 * 66 * 65 ways = 1348621560 ways
The power ball can be picked up from the urn in 26 ways
So, the total number of ways to play the power ball lottery = 1348621560 * 26 = 35064160560
Probability of a win = 1/35064160560
Let the jackpot value be V
We want expected value > 2
[(-2)(35064160559/35064160560) + (V – 2) (1/35064160560)] > 2
On solving, we get V > 140256642240, that is V > $140.26 billion.
The expected winnings are defined as the value of the jackpot multiplied by the probability of...
The Powerball lottery is played twice each week in 44 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 69, and then select a Powerball number from the digits 1 through 26. To determine the winning numbers for each game, lottery officials draw 5 white balls out a drum of 69 white balls numbered 1 through 69 and 1 red ball out...
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In one lottery, a player wins the jackpot by matching all five numbers drawn from white balls (1 through 45) and matching the number on the gold ball (1 through 32). If one ticket is purchased, what is the probability of winning the jackpot? The probability of winning the jackpot with one ticket is (Type an integer or a simplified fraction)
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