Probability question

Question

Suppose I have three coins. Two are fair coins (they have a 50% chance of landing on heads and a 50% chance of landing on tails). One is a weighted coin that has a 75% chance of landing on heads. Suppose I pick one of the coins at random.

Is my answers correct and how can I solve question C

               A)          What is the probability that I picked the weighted coin? = 1/3

               Suppose now that I flip the coin that I picked and it lands on heads. 

               B)           Now what is the probability that I picked the weighted coin? Bayes theorem = 0.428

               Suppose now that I flip it again and it lands on heads again.

               C)           Now what is the probability that I picked the weighted coin? No idea how to go about this

Answer 1

A and B look right. B is actually 3/7 so rounding to 3 s.f. would give you 0.429

C.

Use Bayes thm again

P(Weighted given 2 heads) = [P(2 heads given coin is weighted) * P(Weighted)] / P(2 Heads)

= [(3/4)² * 1/3 ] / [ (2/3)(1/2)² + (1/3)(3/4)² ]

Since you got B this should look familiar. Study the differences between B and C and I think you'll get it