# Find probability the remaining coin is biased???

Here is the layout of the question:

3 coins, 2 are fair but the third is biased with a probability $$4/7$$ for heads. You randomly choose one of these coins, tossing it 10 times, and obtain 5 heads 5 tails. You then choose a different coin, again toss 10 times, and obtain 4 heads 6 tails. What is the probability that the remaining coin is the biased coin?

I have a feeling Bayes theorem could be helpful with this problem but I am unsure how and where to apply it. Is this just the multiplication of two conditional probabilities (namely $$P(\text{first is fair}|5H,5T)$$ and $$P(\text{first is fair}|4H,6T)$$)? Thanks:)