a Mark all outcomes in your sample space that result in an outcome of 7 or 11.
B
b Mark all outcomes in your sample space that result in an outcome of 2, 3 or 12.
C
c The only outcome that cannot happen in order for the game to continue after the first roll is either a win or a loss.
A
a 2/9
B
b 1/9
C
c 2/3
Practice makes perfect
a Let's copy the sample space we drew in 4-10.
Probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes.
P=Number of favorable outcomes/Number of possible outcomes
In total there are 6* 6 =36 possible outcomes. To get the number of favorable outcomes, we have to count every outcome where the sum of the dice show a 7 or 11.
In total there are 8 favorable outcomes. Now we have enough information to determine the probability of winning on the first roll.
P(winning on the first roll): 8/36=2/9
b Similar to Part A, we have to count the outcomes where we lose. Let's mark all outcomes where the sum of the dices show a 2, 3 or a 12.
In total, there are 4 (un)favorable outcomes. Now we have enough information to determine the probability of losing on the first roll.
P(losing on the first roll): 4/36=1/9
c From the exercise, we know that the game continues as long as the player neither wins nor loses. Therefore, the probability that the game continues is the complement to the probability that he either wins or loses.
