A box contains two coins. One is a double-headed coin, and the other is an ordinary coin ( heads on one side, and tails on the other). You take one of the coins out of the box and look at one of the sides. It’s a head. What’s the probability that the other side also contains a head?
If you have not tried to solve it, have a go now. For everyone else the answer is after the break.
When the coin is taken out of the box, there are four possibilities:
Coin Drawn Side Shown Other side
Double headed Heads Heads
Double headed (other side) Heads Heads
Normal coin Heads Tails
Normal coin Tail Heads
The last possibility didn’t occur, so there are three remaining possibilities. Of the three, two of them will show heads on the other side and only one will show tails on the other side. So the probability that the other side of the coin is heads is two thirds.
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