In a single throw of three dice, determine the probability of getting i. total of 5 ii. total of at most 5 ii. a total of at least 5.

Answer

`(i) 1/36 (ii) 5/108`

Explanation

`n(S) = (6 xx 6 xx 6) = 216`
(i) `E_(1) = {(1, 1, 3), (1, 3, 1), (3, 1, 1),(1, 2, 2),(2, 1, 2),(2, 2, 1)}`
`therefore P(E_(1)) = 6/216 = 1/26.`
(ii) `E_(2) = {(1, 1, 1), (1, 1, 2),(1, 2, 1),(2, 1, 1),(1, 1, 3),(1, 3, 1),(3, 1, 1), (1, 2, 2),(2, 1, 2),(2, 2, 1)}`
`therefore P(E_(2)) = 10/216 = 5/108.`