 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2018/discrete-mathematics-continuous-mathematics-and-probability/8/a/i/solution

The single-roll colour probabilities are

1/2

1/3

and

1/6

. There are

3!

possible orders of the three distinct colours, and the independent rolls give each order probability

(1/2) (1/3) (1/6)

. The events are disjoint, so the required probability is

3! \frac{1}{2} \frac{1}{3} \frac{1}{6} = \frac{1}{6} .

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