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Math Help - Powerball odds

  1. #1
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    Powerball odds

    I'm trying to calculate the odds for the Powerball.. They draw 5 balls from the numbers 1-59 and then a Powerball from the numbers 1-35. The posted odds for getting just the Powerball right are 1 in 55.41. I can't get this number. When I tried I said the probability of the firstwhite ball not being correct is 54/59 the next white ball was 54/58, and etc. So the individual odds I used were 54/59, and 54/58, and 54/57, 54/56, 54/55, and 1/35. When I multiply these I don't get the right answer.. What did I do wrong?
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  2. #2
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    Re: Powerball odds

    You appear to be calculating the odds that the first five balls are NOT the numbers selected but the power ball is the number you selected. It would make more sense to multiply the first five numbers by 34/35, the probability that the power ball is not the number you selected and the subtract the product from 1.
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  3. #3
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    Re: Powerball odds

    Yeah I was doing that. The first way to win is to get the Powerball number and only that one correct. So I was finding the odds of not getting any of the first 5 right and then getting the final ball correct
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  4. #4
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    Re: Powerball odds

    Hello, Dawgs1236!

    I'm trying to calculate the odds for the Powerball.
    They draw 5 balls from the numbers 1-59 and then a Powerball from the numbers 1-35.
    The posted odds for getting just the Powerball right are 1 in 55.41. .Not true

    I can't get this number.
    When I tried I said the probability of the first ball not being correct is 54/59,
    . . the next ball was 54/58, etc. . No

    Among the 59 numbers are: 5 Winners and 54 Losers.
    . . We want 5 Losers. .There are: _{54}C_5 ways.
    There are: _{59}C_5 possible outcomes.

    Hence: P(\text{5 Losers}) \:=\:\frac{_{54}C_5}{_{59}C_5}

    The probability of getting the Powerball is \tfrac{1}{35}

    We have: . P(\text{5 losers }\wedge\text{ Powerball}) \:=\: \frac{1,\!581,\!255}{2,\!503,\!193}\cdot\frac{1}{3  5} \:=\:0.018048438

    The odds are: . 0.018\;\!048\;\!438\,:\,0.981\;\!951\;\!566


    Divide by 0.018048438: . 1 : 54.406\;\!456\;\!99

    The odds are approximately . {\color{blue}1 : 54.41}
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  5. #5
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    Re: Powerball odds

    Published results are many factors lower. Match 5 Outcomes = 59C5 = 5,153,532 Winning chance 1
    Match 5 + PB = 59C5*35 = 175223510 Winning chance1
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  6. #6
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    Re: Powerball odds

    Soroban's caculation matches 0 of 5 and the PB
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