SOLUTION: The current Powerball jackpot is estimated to be $193 million. The Powerball lottery is decided every Wednesday and Saturday night by drawing five white balls out of a drum with 6

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Question 1165788: The current Powerball jackpot is estimated to be $193 million. The Powerball lottery is decided every Wednesday and Saturday night by drawing five white balls out of a drum with 69 balls and one red ball out of a drum with 26 red balls. The Powerball jackpot is won by matching all five white balls in any order and the red Powerball. Each ticket costs $2.
What is the expected value for purchasing one ticket for the jackpot?
Answer by ikleyn(52805) About Me  (Show Source):
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The current Powerball jackpot is estimated to be $193 million.
The Powerball lottery is decided every Wednesday and Saturday night by drawing five white balls
out of a drum with 69 balls and one red ball out of a drum with 26 red balls.
The Powerball jackpot is won by matching all five white balls in any order and the red Powerball.
Each ticket costs $2. What is the expected value for purchasing one ticket for the jackpot?
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The total number of all possible quintuples of integer numbers from 1 to 69, with no repeating, is

    C%5B69%5D%5E5 = %2869%2A68%2A67%2A66%2A65%29%2F%281%2A2%2A3%2A4%2A5%29 = 8259888

(the number of combinations).


So, the probability to get the winning ticket is

    P = 1%2F%288259888%2A26%29.


Thus the expected value of this lottery for purchasing one ticket is

    193000000%2F%288259888%2A26%29-2 = -1.101310221  dollars.

Solved.