A favorite casino game of dice “craps” is played in the following manner: A play

Question

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:

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)

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

if the player throws a total of 4 then the next game will end if total of 4 or 7 will appear on the next roll.

numbe of ways a total of 4 can come =3 which are (1,3),(2,2),(3,1)

also number of ways a total of 7 can come =6 which are (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

hence total number of ways that game can end on next roll =3+6 =9

probability that the game ends in the next roll =9/36 =1/4

b)  probability that the game continues after the next roll =1-P( game ends in the next roll)

=1-(1/4 ) =3/4

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