Question

Two different dice are thrown together. Find the probability that the numbers obtained have
(i) even sum, and
(ii) even product.

Answer 1

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)
No pf favourable outcomes = 18
P(even sum) = $\frac{\text{Favourable outcomes}}{\text{Total outcomes}}$
=$\frac{18}{36}=\frac{1}{2}$
(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
P(even product) = $\frac{\text{Favourable outcomes}}{\text{Total outcomes}}$
=$\frac{27}{36}=\frac{3}{4}$