When two dice are rolled, there are 36 possibilities. These can be found by calculating the number of counts.
We are required to find the favor of rolling a sum, which is similar to saying the probability of rolling a given sum.
Recall that the probability of an event occurring is given as:
[tex]\text{Probability = }\frac{Number\text{ of required outcomes}}{\text{Total Number of possible outcomes}}[/tex](a) Sum equaling 8
[tex]\text{Probability = }\frac{5}{36}[/tex](b) Greater than 6
[tex]\begin{gathered} \text{Probability = probability of 7 + probability of 8 + probability of 9 + probability of 10 + probability of 11 + probability of 12} \\ =\text{ }\frac{6\text{ + 5 + 4 + 3 + 2 + 1}}{36} \\ =\text{ }\frac{21}{36} \\ =\text{ }\frac{7}{12} \end{gathered}[/tex](c) Less than or equal to 9
[tex]\begin{gathered} \text{Probability = 1 - Probability of a sum greater than 9} \\ =\text{ 1 - (Probability of 10 + Probablity of 11 + Probability of 12)} \\ =\text{ 1 - }\frac{6}{36} \\ =\text{ }\frac{30}{36} \\ =\text{ }\frac{5}{6} \end{gathered}[/tex](d) That is an odd number
Odd numbers are 1, 3 , 5 , ...
[tex]\begin{gathered} There\text{ are 18 odd numbers} \\ \text{Probability = }\frac{18}{36} \\ =\text{ }\frac{1}{2} \end{gathered}[/tex]