Question

Two different dice are tossed together. Find the probability that

(i) the number on each die is even,
(ii) the sum of the numbers appearing on the two dice is 5.

Answer 1

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

(i) Let E₁ be the event of getting an even number on each die.

These numbers are (2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4) and (6, 6).

Number of Favourable outcomes = 9

∴ P(getting an even number on both dice) = $\mathrm{P}\left({\mathrm{E}}_1\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{outcomes}\mathrm{favourable}\mathrm{to}{\mathrm{E}}_1}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$

= $\frac{9}{36}=\frac{1}{4}$

Thus, the probability of getting an even number on both dice is $\frac{1}{4}$.

(ii) Let E₂ be the event of getting the sum of the numbers appearing on the two dice is 5.

These numbers are (1, 4), (2, 3), (3, 2) and (4, 1)

Number of Favourable outcomes = 4

∴ P(getting the sum of the numbers appearing on the two dice is 5) = $\mathrm{P}\left({\mathrm{E}}_2\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{outcomes}\mathrm{favourable}\mathrm{to}{\mathrm{E}}_2}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$

= $\frac{4}{36}=\frac{1}{9}$

Thus, the probability of getting the sum of the numbers appearing on the two dice is 5 is $\frac{1}{9}$.