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

` (i) 1/4 (ii) 1/9`

Explanation

When two different dice are thrown, then total number of outcomes = 36.
(i) Let ` E_(1)` 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),(6,6)`.
Number of favourable outcomes = 9.
` :. ` P(getting an even number on both dice) ` P(E_(1)) = 9/36 = 1/4`.
(ii) Let ` E_(2)` be the event of getting the sum 5. Then these numbers are ` (1,4),(2,3),(4,1),(3,2)`.
Number of favourable outcomes = 4.
` :. P(E_(2)) = 4/ 36 = 1/ 9 `.