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Raffle winning probability

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  • 15-07-2012 11:39am
    #1
    ozzy jr
    Closed Accounts Posts: 1,519 ✭✭✭


    Help settle an argument please.

    If there's a raffle with 12 million tickets and I have 6, do I have a 2 million to 1 chance of winning? Is it as simple as that?

    Or, are my odds on winning 11,999,994-1.

    It was a usual Saturday night pub discussion! Apologies if this is posted in the wrong forum.


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    #2
    **Timbuk2**
    Moderators, Education Moderators, Motoring & Transport Moderators Posts: 7,395 Mod ✭✭✭✭**Timbuk2**


    The probability of something happening, where events are equally likely is the number of favourable outcomes divided by the number of possible outcomes.

    So in this case it's just 6/12000000


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    #3
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,847 Mod ✭✭✭✭Michael Collins


    Odds and probability are defined slightly differently in maths. So the probability that you will win, assuming everything is random and your tickets are all different etc, is

    [latex] \displaystyle p = \frac{6}{12\hbox{ million}}[/latex]

    as Timbuk2 has said,

    but odds against (which is the way bookmakers do it) are defined

    [latex] \displaystyle \hbox{odds} = \frac{1-p}{p}[/latex]

    so in this case the odds against are

    [latex] \displaystyle \hbox{odds} = \frac{1-\frac{6}{12\hbox{ million}}}{\frac{6}{12\hbox{ million}}} = \frac{11,999,994}{6}[/latex]

    or in bookmaker notation: 11,999,994 – 6 or 1,999,999 – 1.

    So this means you enter the raffle 12 million times, 11,999,994 of those times you lose, 6 times you win - on average, over many many raffles!


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