Question

If two different dice are rolled together, the probability of getting an even number on both dice is 

Options

• \[\frac{1}{36}\]

• \[\frac{1}{2}\]

• \[\frac{1}{6}\]

• \[\frac{1}{4}\]

Answer 1

When two dice are rolled together, all possible outcomes are
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
∴ Total number of outcomes = 36
The favourable outcomes are (2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4) and (6, 6).
So, the number of favourable outcomes are 9.
∴ P(getting even number on both dice) = \[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }}+ = \frac{9}{36} = \frac{1}{4}\]