Question

two dice are thrown together . what is the probability that sum of the numbers on the 2 faces is divisible by 4 or 6.

Answer 1

Dear student
$$\begin{gathered} \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes},\mathrm{n}\left(\mathrm{S}\right)=6\times 6=36 \\ \mathrm{Let}\mathrm{E}\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{that}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{number}\mathrm{on}\mathrm{two}\mathrm{faces}\mathrm{is}\mathrm{divisible}\mathrm{by}4\mathrm{or}6. \\ \mathrm{Then}, \\ \mathrm{E}=\left\{\left(1,3\right),\left(1,5\right),\left(2,2\right),\left(2,4\right),\left(2,6\right),\left(3,1\right),\left(3,3\right),\left(3,5\right),\left(4,2\right),\left(4,4\right),\left(5,1\right),\left(5,3\right),\left(6,2\right),\left(6,6\right)\right\} \\ \mathrm{So},\mathrm{n}\left(\mathrm{E}\right)=14 \\ \mathrm{So},\mathrm{P}\left(\mathrm{E}\right)=\frac{\mathrm{n}\left(\mathrm{E}\right)}{\mathrm{n}\left(\mathrm{S}\right)}=\frac{14}{36}=-\frac{7}{18} \end{gathered}$$
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