Probability Puzzle

ray giraffe

You have 2 boxes: Box A and Box B.

In Box A there are 2 gold coins and 1 silver coin.

In Box B there are 2 silver coins and 1 gold coin.

You choose a box at random, and then choose a coin at random from that box.

Assuming that the coin you picked was gold, what is the probability that there is exactly 1 other gold coin in the box you picked?

My first answer was [latex]\frac{1}{2}[/latex] but the correct answer is [latex]\frac{2}{3}[/latex]

I wonder how could you reword the question to make the answer [latex]\frac{1}{2}[/latex]?

locum-motion

Explanation, as I understand it:

Imagine that each coin has a number, 1,2,3 are in box A, and 4,5,6 are in Box B.

There are 6 possible choices:
1G
2G
3S
4G
5S
6S

If you have randomly picked a gold coin, you have chosen either 1, 2 or 4 (which is a 50:50 chance)

Which of these options include "exactly 1 other gold coin in the box you picked"?

1 does.
2 does.
4 does not.

So, 2/3 have, and 1/3 has not.

As to how you would reword the question:
How about "Forget that coin. Randomly choose a box again. What are the chances that the new box has 3 coins in it?"