Question

If two dice are rolled one time, find the probability of getting these results. Enter your answers as fractions or decimals rounded to 3 decimal places.(b) A sum of 2 or 9

Answer 1

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;

`Pr(2\text{ or 9)=Pr(sum of 2)+Pr(Sum of 9)}`

Next, we can get those probabilities;

`\begin{gathered} Pr(\text{Sum of 2)=}Pr(1\text{ on 1st toss)}* Pr(1\text{ on 2nd toss)} \\ =(1)/(6)*(1)/(6) \\ =(1)/(36) \end{gathered}`

and;

`\begin{gathered} Pr(\text{Sum of 9) =Pr}(3\text{ then 6) + Pr(6 then 3) + Pr(4 then 5) + Pr(5 then 4)} \\ =((1)/(6)*(1)/(6))+((1)/(6)*(1)/(6))+((1)/(6)+(1)/(6))+((1)/(6)+(1)/(6)) \\ =(4)/(36) \\ =(1)/(9) \end{gathered}`

Then the total probability becomes;

`\begin{gathered} Pr(2\text{ or 9)=Pr(sum of 2)+Pr(Sum of 9)}=(1)/(36)+(1)/(9) \\ =(1)/(36)+(4)/(36) \\ =(5)/(36) \end{gathered}`

Therefore, If two dice are rolled one time, find the probability of getting a sum of 2 or 9 is 5/36