Two different dice are rolled together. Find the probability of getting a doublet.

Options

A. `1/6`
B. `1/2`
C. `3/4`
D. `5/6`

Answer

A

Explanation

When two dice are thrown simultaneously, 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),(4,5),(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).
Number of all possible outcomes = 36.
(i) Let `E_(1)` be the event of getting two numbers whose sum is 5.
Then, the favourable outcomes are (1,4),(2,3),(3,2),(4,1).
Number of favourable outcomes = 4.
`:.` P (getting two numbers whose sum is 5) = `P(E_(1)) = 4/36 = 1/9`.
(ii) Let `E_(2)` be the event of getting a even numbers on both dice.
Then, the favourable outcomes 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 even number on both dice ) = `P(E_(2)) = 9/36 = 1/4`.
(iii) Let `E_(3)` be the event of getting a doublet.
Then, the favourable outcomes are
(1,2),(2,2),(3,3),(4,4),(5,5),(6,6).
Number of favourable outcomes = 6.
`:. ` P(getting a doublet ) = `P(E_(3)) = 6/36 = 1/6`.