Re: Bias coin

In article
<15888415.1194017792043.JavaMail.jakarta@xxxxxxxxxxxxxx
orum.org>,
Yves <sunder_1600@xxxxxxxxx> wrote:

Any tips will do. Thanks.

One out of 1000 coins always gives heads, you flip a coin and get heads 10 times, what is probability that it is biased?

Define the events
B: we selected the biased coin at the beginning
F: we selected a fair coin at the beginning

T: A coin selected from the population gives ten out of ten heads.

We want to find Pr(B|T).

Pr(B & T) = Pr(B|T).Pr(T) = Pr(T|B).Pr(B)
= Pr(B)
so
Pr(B)
Pr(B|T) = ---------------------
Pr(B) + Pr(F).Pr(T|F)

We can get ten heads in two ways.
One way is choosing the biased coin,
and one way is choosing a fair coin.
Pr(T) = Pr(B).Pr(T|B) + Pr(F).Pr(T|F).
= Pr(B) + Pr(F).Pr(T|F).

Pr(T|F) = 1/2^10

Pr(B)
Pr(B|T) = ---------------------
Pr(B) + Pr(F).Pr(T|F)

1
= --------------------------
1 + Pr(T|F).Pr(F)/Pr(B)

1
= --------------
1 + 999/2^10

= 0.5062

--
Michael Press
.

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