### Number 231 of a series

There are two treasure chests, both closed. One chest contains 100 gold coins. The other contains 50 gold coins and 50 silver coins.

You randomly chose a chest to open, and you do not look inside, but you remove a coin and close the lid. You look at the coin in your hand, and it is gold. What is the probability you chose the chest with 100 gold coins?

Post your answer in the comments section below.

## Update and Solution

This is a problem in conditional probabilities. What is the probability of A if B is true? It’s written this way.

The probability of A given B is the probability of B given A times the probability of A and divided by the probability of B

A is you chose the chest with 100 gold coins.

B is you pulled a gold coin out of one of the chests.

From the get-go the probability of pulling a gold coin is 3/4.

So P(B) = 1/4

P(B | A) is 1. If you choose the 100% gold chest you are 100% likely to draw a gold coin.

So the answer is ½/¾ = 2/3.

50%

75%

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Typo alert: P(B) = 3/4, not 1/4. The correct value of 3/4 is used in the final line of the solution, but 1/4 is used earlier.

Kenneth, thanks much. I made the fix.