Re: Powerball odds
- From: "mensanator@xxxxxxxxxxx" <mensanator@xxxxxxx>
- Date: 6 Oct 2005 14:24:22 -0700
Ted wrote:
> I'm looking at the odds to win on the Powerball website, and something
> doesn't add up.
>
> Picking 5 white balls in any order - numbered 1-55 - and then 1 red
> ball - numbered 1-42 - produces a winner.
>
> So (55/6)*(55/5)*(54/4)*(53/3)*(52/2)*(51/1) {for white balls}
That's not quite right, it evaluates to
31888642.5
whereas the correct formula (55*54*53*52*51)/(5*4*3*2)
evaluates to
3478761
> * 42
> {for red ball} = 146,107,962.
Which is correct, meaning you didn't actually use the
wrong equation.
> That equals what is stated on the
> powerball website.
>
> However, they state that the odds of hitting the 5 white balls, without
> hitting the powerball are 3,563,608.83, which coincidentally is
> (146,107,962 / 41).
>
> Shouldn't the odds of hitting the 5 white balls be 3,478,761 and not
> 3,563,608.83??
No, 3478761 is the number of combinations of white balls
without the red ball. To odds to win are
1 1
------- * ---
3478761 42
Now, if you have 1 chance in matching the red ball,
you must then have 41 chances of not matching it.
So the odds of getting all 5 white AND missing the
red are
1 41
------- * ---
3478761 42
or
41 1
--------- = ----------
146107962 3563608.83
>
> http://www.powerball.com/powerball/pb_prizes.asp
.
- References:
- Powerball odds
- From: Ted
- Powerball odds
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