Question

Two different dice are rolled simultaneously. Find the probability that the sum of the numbers on the two dice is 10.

Answer 1

When two different dice are thrown, then total number of outcomes = 36.

Let E₁ be the event of getting the sum of the numbers on the two dice is 10.

These numbers are (4, 6), (5, 5) and (6, 4).

Number of Favourable outcomes = 3

∴ P(getting the sum of the numbers on the two dice is 10) = $\mathrm{P}\left({\mathrm{E}}_1\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{outcomes}\mathrm{favourable}\mathrm{to}{\mathrm{E}}_1}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$

= $\frac{3}{36}=\frac{1}{12}$

Thus, the probability of getting the sum of the numbers on the two dice is 10 is $\frac{1}{12}$.