Chance of winning at Craps A favorite casino game of dice cr

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:

What is the probability that a player wins the game on the first roll of dice?

What is the probability that a player loses the game on the first roll of dice?

If the player throws a total of 4 on the first roll, what is the probability that the player wins in the next roll?

If the player throws a total of 4 on the first roll, what is the probability that the player loses in the next roll?

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?

Solution

What is the probability that a player wins the game on the first roll of dice?

There are 36 outcomes.

There are 6 ways to get a 7, and 2 ways to get an all.

Thus,

P(win on first roll) = (6+2)/36 = 2/9 = 0.222222 [answer]

********************

What is the probability that a player loses the game on the first roll of dice?

There is 1 way to get a 2, and 2 ways to get a 3.

Thus,

P(lose on first roll) = (1+2)/36 = 1/12 = 0.08333333 [answer]

********************

If the player throws a total of 4 on the first roll, what is the probability that the player wins in the next roll?

There are 3 ways to produce a 4.

Thus,

P(win on next roll) = 3/36 = 1/12 or 0.08333333 [answer]

*************************

If the player throws a total of 4 on the first roll, what is the probability that the player loses in the next roll?

There are 6 ways to get a 7 on the next roll, in which he loses.

Thus,

P(lose on next roll) = 6/26 = 1/6 or 0.1666667 [answer]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!