question_answer

Two different dice are thrown together. Find the probability that the numbers obtained have

(i) even sum, and

(ii) even product.

Answer:

When two different dice are thrown together

Total outcomes \[=6\times 6=36\]

(i) For even sum ? Favourable outcomes are

(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6)

Favourable outcomes = 18

\[\text{P}\,\text{(even}\,\,\text{sum)=}\frac{\text{Favourable}\,\,\text{outcomes}}{\text{Total}\,\,\text{outcomes}}\]

\[\text{=}\frac{18}{36}=\frac{1}{2}\]

(ii) For even product ? Favourable outcomes are (1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4,6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3). (6, 4), (6, 5), (6, 6),

No. of favourable outcomes = 27

\[\text{P}\,\text{(even}\,\,\text{product)=}\frac{\text{Favourable}\,\,\text{outcomes}}{\text{Total}\,\,\text{outcomes}}\]

\[\text{=}\frac{27}{36}=\frac{3}{4}\]