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put this solution on YOUR website! Tom has three coins. Two are fair and one is an unfair coin weighted so that
heads is five times as likely as tails. He selects one of the coins at random
and flips it.
What is the probability it comes up tails?
We need to first calculate the probabilities for the unfair coin:
P(H) = 5∙P(T)
P(H) + P(T)=1
P(T) = 1-P(H)
P(T) = 1-5∙P(T)
6P(T)= 1
P(T) = 1/6
P(H) = 5∙(1/6)
P(H) = 5/6
There are two possibilities
1. He selects a fair coin and it comes up tails
P(fair coin) = 2/3
P(tails on fair coin) = 1/2
P[(selects fair AND tails on fair coin) OR (selects unfair AND tails on unfair coin)]
AND means we multiply and OR means we add.
(2/3)(1/2) + (1/3)(1/6)
That calculates to be 7/18
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If it does come up tails, what is the probability it was a fair coin?
P(fair|tail) = P(fair AND tail)/P(tail) = [(2/3)(1/2)]/(7/18) = 6/7
Edwin
