SOLUTION: 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

Question 1124560: 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 heads?

If it does come up heads, what is the probability it was a fair coin?

Enter your answers as whole numbers or fractions in lowest terms.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
probability of three coins coming up heads are 0.5, 0.5, and (5/6) or 0.8333
the expected value of heads is (1/2)(1/3)*2+(5/6)(1/3)=1/3+(5/18)=(11/18) ANSWER
P(Fair|Heads)=P(Fair)*P(H|F)/P(H)
=(2/3)*(1/2)/(11/18)
=(1/3)(18/11)=18/33 or 6/11 ANSWER
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