Question

2 dice are thrown simultaneously , what is probability that sum of numbers appearing on dice is :a prime number , 7 & 1

Answer 1

Dear student,

$$\begin{gathered} ProbabilityP\left(E\right)=\frac{Totalnumberofdesiredeventsn\left(E\right)}{Totalnumberofeventsn\left(S\right)} \\ Heretwodicearethrownsimul\tan eously. \\ so, \\ Totalnumberofeventsn\left(S\right)=6\times 6=36 \\ Gettingaprimenumberasasum,wegetcombination=\left\{1,1\right\}\left\{2,1\right\}\left\{1,2\right\} \\ \left\{1,4\right\}\left\{1,6\right\}\left\{2,3\right\}\left\{2,5\right\}\left\{3,2\right\}\left\{3,4\right\}\left\{4,1\right\}\left\{4,3\right\}\left\{5,2\right\}\left\{5,6\right\}\left\{6,5\right\}and\left\{6,1\right\} \\ Totalno.ofcombinations=15 \\ n\left(E\right)=15 \\ So,Probabilityofgettingaprimenumberassum=\frac{15}{36}=\frac{5}{12} \end{gathered}$$
Regards