Answer
The sample outcomes contained in the event “Shooter wins with a point of 9” are
\[S=\left\{ \left( 9,9 \right),\text{ }\left( 9,\text{ no }7\text{ or no }9,\text{ }9 \right),\text{ }\left( 9,\text{ no }7\text{ or no }9,\text{ no }7\text{ or no }9,\text{ }9 \right),\text{ }.... \right\}\]
Work Step by Step
In the game of craps, the shooter rolls two dice and wins with a point of 9. His first roll is 9 and he must roll the dice again and again, as often as is necessary until the initial sum, 9 is repeated (shooter wins) and no 7’s are rolled (shooter loses).
In order for the shooter to win with a point of 9, one of the following sequences of sums must be rolled: (9,9), (9,2,9), (9,3,9), (9,4,9), (9,5,9), (9,6,9), (9,8,9), (9,10,9), (9,11,9), (9,12,9), (9,2,2,9)………
Therefore, the sample space of the event “Shooter wins with a point of 9” can be written as:
\[S=\left\{ \left( 9,9 \right),\text{ }\left( 9,\text{ no }7\text{ or no }9,\text{ }9 \right),\text{ }\left( 9,\text{ no }7\text{ or no }9,\text{ no }7\text{ or no }9,\text{ }9 \right),\text{ }.... \right\}\]
