Please write on paper and show the steps to solving this. Thanks!

Question: A 2Player game is to be played in 5 rounds. whichever player gets the first wins 3 of the 5 rounds will get the prize. However, the game was halted for some reason after the 3rd round, with two wins for Player A and one win for Player B. How should the two players divide the money prize? Method 1 {Simple Method}: Let p be the probability that Player A wins a round. Ifthe game were to be continued, the probability that Player A collects the prize is the probability that he wins one more round before Player B wins 3 rounds. This is p + (1 13);). There is no reason to believe that p i 0.5. So 33 + (1 19);} = 0.75. Therefore, 25% of the money prize should go to Player A. Method 2 {Max likelihood Method): Because PlayerA won 2 out of 3 rounds, the maximum likelihood value ofp is 2/3. So by replacing p by 2/3 in p + (1 39);? we get approximately 0.89. Hence, 89% of the money prize should go to Player A. Method 3 {YourTurn}: 1a) State an appropriate prior f(p). 1b} Find the Posterior of 3:) given that Player A won 2 times and Player B won only 1 time. 1c) Find E[p + p(1 10)] by using the Posterior for 33 that you found in (1b), and discuss your answer compared to the two previous Methods (Method 1 and Method 2)