Question # 8 Player A rolls a die with 7 on four sides and 11 on two sides. Play
ID: 3376647 • Letter: Q
Question
Question # 8 Player A rolls a die with 7 on four sides and 11 on two sides. Player B flips a coin with 6 on one side and 10 on the other. Assume both are fair and independent of each other. Use a table or a tree diagram. A. State the sample space B. Suppose the winner is the player with the higher number showing. Explain who would you rather be. C.If player A receives $0.25 for every win, what should player B receive for every win to make the game fair? A fair game is each player breaks even. D. Suppose player A receives S0.70 from Player B when the 7 shows and $1.10 when the 11 shows, while Player B receives $0.60 from player A when the 6 shows and $1.00 when the 10 shows. Using statistics explain whom you would rather be.Explanation / Answer
A) Sample Space
Above is the sample size data when both player fillped the coin and rolled the coin individually, earlier no in the above sample space represent Die possible outcome and later one denotes Coin flliped outcome e.g (7,6) here 7 is Die outcome and 6 is Coin outcome, total possible outcome is 12.
B) If the player who is winning is having the higher no that means from above sample space it is clear that i would like to be on the player 1 side as he is having maximum possiblity of gaining higher number. Apart from 12 sample space the probaility of winning player 1 as having Higher no is 8/12 =0.667, and player B will be having probability of winning is 4/12 = 0.333.
C) As in question it is asked that if Player 1 wins he will get $0.25 hence the expected value of total win by player will be 0.667 * 0.25 = $0.1167 in order to be fair game this game must cost $0.1167 , hence player 2 , as his probability is 0.333 , in order to make game fair he should win 0.1167/0.33 = $0.35 per game.
D)Probabilty for player 1
From above data EV = 0.667* 0.70+ 0.33*1.10
= 0.4670 + 0.363 = $ 0.83.
Probaibility for Player 2
From above probaility table
E.V = 0.60 *0.50+ 1.00* 0.5 =0.3 +0.5 = $ 0.80
Hence from above calculation i would rather like to be on Player 1 side as more laible to earn.
7,6 7,6 7,6 7,6 11,6 11,6 7,10 7,10 7,10 7,10 11,10 11,10