Question

Two dice are thrown together. The probability of getting the same number on both dice is

Options

• \[\frac{1}{2}\]

• \[\frac{1}{3}\]

• \[\frac{1}{6}\]

• \[\frac{1}{12}\]

Answer 1

When two dice are thrown 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 (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6).
So, the number of favourable outcomes are 6.
∴ P(getting the same number on both dice) = \[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{6}{36} = \frac{1}{6}\]