Question

Each of three identical jewelry boxes has two drawers. in each drawer of the first box there is a gold watch. in each drawer of the second box there is a silver watch. in one drawer of the third box there is a gold watch while in the other there is a silver watch. if we select a box at random, open one of the drawers and find it to contain a silver watch, what is the probability that the other drawer has the gold watch?

Answer 1

Let's call
`G_1,\ G_2` the two drawers of the first box, both containing gold.

Let's call
`G_3,\ S_1` the two drawers of the second box, one containing silver, and one containing gold.

Let's call
`S_2,\ S_3` the two drawers of the third box, both containing silver.

If you opened a drawer containing silver, you opened either
`S_1,\ S_2` or
`S_3`.

If you opened
`S_1`, the other drawer is
`G_3`, and thus contains gold.

If you opened
`S_2`, the other drawer is
`S_3`, and thus contains silver.

If you opened
`S_3`, the other drawer is
`S_2`, and thus contains silver.

So, in one case out of three, the other drawer containes gold, and the probability is
`(1)/(3)`