Question

4. Rolling Two Dice: If two dice are rolled one time, find the probability of 

getting these results. 

a. A sum of 9 

b. A sum of 7 or 11 

c. A sum greater than or equal to 10

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hdashline 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hdashline 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hdashline 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hdashline 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ \hdashline 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hdashline \end{array}$$

a.

$$P(Sum=9)=\dfrac{4}{36}=\dfrac{1}{9}$$

b.

$$P(Sum=7\ or\ Sum=11)=P(Sum=7)$$

$$+P(Sum=11)=\dfrac{6}{36}+\dfrac{2}{36}=\dfrac{2}{9}$$

c.

$$P(Sum\ge10)=P(Sum=10)+P(X=11)$$

$$+P(X=12)=\dfrac{3}{36}+\dfrac{2}{36}+\dfrac{1}{36}=\dfrac{1}{6}$$