is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture 
If the ratio of coffee and cocoa in the mixture 
is 
then the ratio of cocoa in mixture 
Y by
The solution is wrong.
2/27 probability is for three flips, so the 'correct' answer from this solution should have been 27/2 * 3= 81/2 flips.
The correct answer for THT is 31/2.
The correct solution:
Let
be the expected number of flips to get HTT after getting an H.
Then = (case TT) 1/3 * 1/3 * 2 + (case TH) 1/3 * 2/3 * (+2) + (case H) 2/3 * (+1)
= 12
E = (case H) 2/3* (1+) + (case T) 1/3*(1+E)
E=27/2
The only argument that can be made for this solution is the answer of 1/P is correct for sequences of H followed by Ts.
2/27 probability is for three flips, so the 'correct' answer from this solution should have been 27/2 * 3= 81/2 flips.
The correct answer for THT is 31/2.
The correct solution:
Let
be the expected number of flips to get HTT after getting an H.Then
= (case TT) 1/3 * 1/3 * 2 + (case TH) 1/3 * 2/3 * (+2) + (case H) 2/3 * (+1)= 12E = (case H) 2/3* (1+
) + (case T) 1/3*(1+E)E=27/2
The only argument that can be made for this solution is the answer of 1/P is correct for sequences of H followed by Ts.
