John has two coins, one fair and the other unbalanced so that the probability of its coming up heads is 6/7. H

THIS IS THE FULL PROBLEM

John has two coins, one fair and the other unbalanced so that the probability of its coming up heads is 6/7. He picks one of the coins at random, tosses it, and it comes up heads. What is the probability that he picked the unbalanced coin? (Enter the probability as a fraction.)

I have no idea how to solve this problem! Please help! :)

taryn -

This problem is set up perfectly for a "tree diagram".

The first two branches are FAIR and UNFAIR -- these are random so assign 0.50 to each

Next, under the FAIR branch, make two more branches: Head 0.5 and Tail 0.5

Similarly, under UNFAIR branch, make two more branches: Head 6/7 and Tail 1/7

Now multiply out your branches to get the probability of heads:

P(H|FAIR) = 1/2 * 1/2 = 1/4

P(H|UNFAIR) = 1/2 * 6/7 = 6/14 = 3/7

P(UNFAIR|H) = (3/7) / [(1/4) + (3/7)] = 12/19

Hope that helped