Raffle winning probability

ozzy jr

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.

**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

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!