Question:
Two different dice are thrown together. Find the probability that the numbers obtained have
(i) even sum
(ii) even product.
Solution:
Total number of possible outcomes is 36.
(i) The favorable 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).
$P($ the sum is even $)=\frac{18}{36}=\frac{1}{2}$
(ii) The favorable 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).
$\mathrm{P}($ the product is even $)=\frac{27}{36}=\frac{3}{4}$