Simple confidence question..

1800GAMBLER · #1 09-21-2003, 11:10 PM

Probability of being dealt aces is 1/221. How would i work out the confidence that after i dealt 221 starting hands one of those was AA.

Is it 1- [[1-(1/221)]^221] ?

More questions to follow if it is.

Thanks.

irchans · #2 09-21-2003, 11:53 PM

You got it right!

1 - ((1 - (1/221))^221.) = .632954

which is almost 1- 1/e = .632121.

1800GAMBLER · #3 09-22-2003, 05:22 PM

The 'more questions' part i don't need to ask. But how does exp. get involved in this? Just an exp. graph when you model it? and the 1/e is the gradient, or am i way off?

Ed Miller · #4 09-22-2003, 06:34 PM

The limit as n -> inf of [1 -1/n]^n = 1/e

Hopefully it should be intuitive to you why e is involved... this is exactly the same problem as calculating the half-life of a radioactive substance. So it wouldn't make sense for the answer to be anything else...