contestada

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?

Respuesta :

Let's call [tex] G_1,\ G_2 [/tex] the two drawers of the first box, both containing gold.

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

Let's call [tex] S_2,\ S_3 [/tex] the two drawers of the third box, both containing silver.

If you opened a drawer containing silver, you opened either [tex] S_1,\ S_2 [/tex] or [tex] S_3 [/tex].

If you opened [tex] S_1 [/tex], the other drawer is [tex] G_3 [/tex], and thus contains gold.

If you opened [tex] S_2 [/tex], the other drawer is [tex] S_3 [/tex], and thus contains silver.

If you opened [tex] S_3 [/tex], the other drawer is [tex] S_2 [/tex], and thus contains silver.

So, in one case out of three, the other drawer containes gold, and the probability is [tex] \frac{1}{3} [/tex]