Question

A bag contains 1 fair and 1 double (heads) sided coin,we choose a random coin and flip it once, and it comes up heds. What is the prob the coin you choose was the fair coin

Answer 1

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A bag contains 1 fair and 1 double (heads) sided coin,we choose a random coin and flip it once, and it comes up heds. What is the prob the coin you choose was the fair coin.

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Here you got two coins. One is a fair one and the other one is biased.

For the fair coin, P(H)=P(T)=1/2 and for the biased one, P(H)=1 &P(T)=0.

Now we apply the Bayes' theorem , Which says, P(A|B)=P(A∩B)/P(B)

Here A=Choosing the biased coin and B=Getting the outcome Head after flipping

So A∩B=Gettign head from the biased coin.

$\rule{300}{2}$

Now, P(A∩B)=P(choosing the biased coin)*P(getting an head from the biased coin)=1/2*1=1/2

P(B)=P(choosing the fair coin and Getting head)+P(Choosing the biased coin and getting head)=(1/2*1/2)+(1/2*1)=3/4

So P(A|B)=(1/2)/(3/4)=2/3.

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