Question

Die A has orange on one face and blue on five faces, Die B has orange on two faces and blue on four faces, Die C has orange on three faces and blue on three faces. All are fair dice. If the three dice are rolled, find the probability that exactly two of the three dice come up orange.

Answer 1

`(2)/(9)`

Explanation:

There are 3 ways to have exactly two orange:

A, B orange; C blue -
`(1)/(6)* (2)/(6)* (3)/(6)`

=
`(1)/(36)`

A, C, orange; B blue -
`(1)/(6)* (3)/(6)* (4)/(6)`

=
`(1)/(18)`

B, C, orange; A blue -
`(2)/(6)* (3)/(6)* (5)/(6)`

=
`(5)/(36)`

The probability of exactly two of the three dice come up orange

=
`(1)/(36) + (1)/(18) +(5)/(36)`

=
`(2)/(9)`