Answer the following question show your proof and explain th

Answer the following question, show your proof, and explain the proof:

I tell you that I have two coins. One is a fair coin, equally likely to come up heads or tails; the other is a two-headed coin. Without telling you whether it is the fair or unfair coin, a take a particular coin C and flip it twice. Both times it comes up heads. What is the probability that I have flipped the fair coin?

Solution

Dear student

Thank you for using Chegg !!

Probability of getting a head with coin 1 is (1/2)

Probability of getting head with coin 2 is 1

Now Given that event HH (Two headshas occured)

P1 : Probability with fair Coin = (1/2)(1/2)

P2 : Probability with unfair coin = (1)(1)

Given the event HH has occurred, you can say the chances of it being coin 1 versus it being coin2 is P1:P2
= 1/4

Which means that the probability that it\'s the First coin = P1/(P1+P2)

=1/5

Hence solved