Bite-sized brain teaser to solve in a minute or less.
The Gold Gamble
Category: Logical Probability
You’re shown 3 sealed boxes:
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Box A contains 2 gold coins
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Box B contains 2 silver coins
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Box C contains 1 gold and 1 silver coin
You randomly pick a box and randomly pull out one coin from that box.
It’s gold.
What’s the probability the second coin in that box is also gold?
A) 1/2
B) 2/3
C) 1/3
Solution
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There are a total of 6 coins distributed across the three boxes. Let's label them to track their positions.
Box A: G1, G2
Box B: S1, S2
Box C: G3, S3
You have already pulled one coin, and it is gold. The only possible coins you could be holding right now are: G1 from Box A G2 from Box A G3 from Box C The question asks for the probability that the second coin in that same box is also gold. Let's look at what is left in the box for each of our 3 possible scenarios:
If you picked G1, the other coin in the box is G2
If you picked G2, the other coin in the box is G1
If you picked G3, the other coin in the box is S3
In 2 out of the 3 equally likely scenarios, the remaining coin is gold.
Answer: B) 2/3
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