Show your calculation and give your answer in the fraction form and in the decim

Question

Show your calculation and give your answer in the fraction form and in the decimal form to receive full credit. Chance of winning at "Craps" A favorite casino game of dice "craps" is played in the following manner:A player starts by rolling a pair of balanced dice. If the roll (the sum of two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results in a 2 or 3 (called "craps") the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (in which case the player wins) or until a 7 occurs (in which case the player loses). When answering the following questions, you can use this outcome chart for the roll of two dice: a. What is the probability that a player wins the game on the first roll of dice? b. What is the probability that a player loses the game on the first roll of dice? c. If the player throws a total of 4 on the first roll, what is the probability that the player wins in the next roll? d. If the player throws a total of 4 on the first roll, what is the probability that the player loses in the next roll? e. If the player throws a total of 4 on the first roll what is the probability that the game ends in the next roll? (win or lose) f. If the player throws a total of 4 on the first roll, what is the probability that the game continues after the next roll?

Explanation / Answer

as probabilty of getting a sum X has following probabilty

a) probabilty that player wins on first roll =(7 or 11 came) =(6+2)/36=8/36 =2/9

b)probabilty that player loses on first roll =(2 or 3 came) =(1+2)/36=3/36=1/12

c) probabilty that player wins in next roll =P(4 came) =3/36=1/12

d)probabilty that player loses in next roll =P(7 came) =6/36=1/6

e)probabilty that game ends in next roll=(1/12+1/6)=3/12 =1/4

f)probabilty that game continues in next roll=1-1/4=3/4

x P(X) 2 1/36 3 2/36 4 3/36 5 4/36 6 5/36 7 6'36 8 5/36 9 4/36 10 3/36 11 2/36 12 1/36

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