Question

We roll a pair of dice once and are given that the two numbers that occur are not the same. Compute the following probabilities:

• i) the sum is 7

• ii) the sum is 4

• iii) the sum is 12

Answer 1

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

i)

$$P(sum=7)=\dfrac{6}{30}=\dfrac{1}{5}$$

ii)

$$P(sum=4)=\dfrac{2}{30}=\dfrac{1}{15}$$

iii)

$$P(sum=12)=0$$