Planetarium coins puzzle (explanation)
The mathemagician tosses a pair of ordinary coins, glances at them and tells you one is a head. What are the odds that the other one is a head, too?
![Mathemagician]](graphics/math.jpg)
Answer:
the odds are 2 to 1 against.
When the mathemagician tosses the coins, there are four ways they can come down. He said one was a head, so the coins didn’t land as a pair of tails — that leaves only three options. And of these three options, two of them are the single head that the mathemagician saw — the other coin can only be a head if he threw a pair of heads. That’s one in three.
| this coin | that coin | one is a head? | other is a head? |
|---|---|---|---|
| tail | tail | no (didn’t happen) | |
| head | tail | yes | no |
| tail | head | ||
| head | head | yes | |
This puzzle is just a warm-up.
It doesn’t form part of Planetarium itself.
