If two dice are rolled one time, find the probability of getting these results.
i. A sum of 2 or 9.
To find the probability of obtaining a sum of 2 or 9. We list the possible sums of 2 and 9.
The combinations that could result in a sum of 2 or 9 is;
Now we can compute the probability;
[tex]Pr(2\text{ or 9)=Pr(sum of 2)+Pr(Sum of 9)}[/tex]
Next, we can get those probabilities;
[tex]\begin{gathered} Pr(\text{Sum of 2)=}Pr(1\text{ on 1st toss)}\times Pr(1\text{ on 2nd toss)} \\ =\frac{1}{6}\times\frac{1}{6} \\ =\frac{1}{36} \end{gathered}[/tex]
and;
[tex]\begin{gathered} Pr(\text{Sum of 9) =Pr}(3\text{ then 6) + Pr(6 then 3) + Pr(4 then 5) + Pr(5 then 4)} \\ =(\frac{1}{6}\times\frac{1}{6})+(\frac{1}{6}\times\frac{1}{6})+(\frac{1}{6}+\frac{1}{6})+(\frac{1}{6}+\frac{1}{6}) \\ =\frac{4}{36} \\ =\frac{1}{9} \end{gathered}[/tex]
Then the total probability becomes;
[tex]\begin{gathered} Pr(2\text{ or 9)=Pr(sum of 2)+Pr(Sum of 9)}=\frac{1}{36}+\frac{1}{9} \\ =\frac{1}{36}+\frac{4}{36} \\ =\frac{5}{36} \end{gathered}[/tex]
Therefore, If two dice are rolled one time, find the probability of getting a sum of 2 or 9 is 5/36
