 # Quiz Question

### 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?

## 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.

## 5 thoughts on “Quiz Question”

1. Helen cutler says:

50%

2. Michael McCants says:

75%

3. Pingback: Quiz Question | Skeptical Analysis

4. Kenneth Almquist says:

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.

• John Blanton says:

Kenneth, thanks much. I made the fix.

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