Question

1. in a game of craps using two dice, a person wins on the first roll if a 7 or an 11 is rolled. find the probability of winning on the first roll.

Explanation:

Step1: Find total number of outcomes

When two dice are rolled, each die has 6 possible outcomes. So the total number of outcomes when two dice are rolled is $n(S)=6\times6 = 36$.

Step2: Find number of ways to roll a 7

The possible combinations to get a sum of 7 are $(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$. So the number of ways to roll a 7 is $n(7)=6$.

Step3: Find number of ways to roll an 11

The possible combinations to get a sum of 11 are $(5,6),(6,5)$. So the number of ways to roll an 11 is $n(11)=2$.

Step4: Find number of favorable outcomes

The number of favorable outcomes (rolling a 7 or 11) is $n(A)=n(7)+n(11)=6 + 2=8$.

Step5: Calculate the probability

The probability $P(A)=\frac{n(A)}{n(S)}=\frac{8}{36}=\frac{2}{9}$.

Answer:

$\frac{2}{9}$