A ticket is to be drawn at random from a box containing eigh

A ticket is to be drawn at random from a box containing eight tickets. Each ticket should
have two numbers; however, three tickets have one blank space:
(1, {), (1, 2), (1, 2), (1, 3), (3, 1), (3, 2), (3, {), (3, {)
What numbers should go in the first, second, and third blank spaces to make the first number
of the ticket drawn and the second number of the ticket drawn independent?

Solution

To make this independent, all we do is we make sure that what ever number comes up in first part of ticket, it does not change distribution of numbers in second part. Note that first 4 tickets have 1 and last four tickets have 3 as first part. We only need to super impose second numbers, which should be: 1,2,2,3,1,2,2,3 (visible). Knowledge about first number does not change distribution of second, and vice a versa.

Thus the missing numbers are: 1,2,3