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 two dice is 5.[CBSE 2014]

Total numbers of elementary events are: 6 x 6 = 36

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

The favourable combinations are: (2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)

Then, the number of favourable outcomes are = 9

∴ P (getting even number on both dice) =P (E) = 9/36 = 1/4

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

The favourable combinations for event are: (1, 4), (2, 3), (3, 2), (4, 1)

Then, the numbers of favourable combinations = 4

∴ P (sum of numbers appearing on two dice is 5) =P (E) = 4/36 = 1/9