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Let’s say you flip two coins. There are going to be three different possible combinations:
So then what are the odds of each possibility? A lot of people think that they’re all the same. Since there are three possibilities, they each have a 1/3 (or 33.3%) chance of happening.
But this actually isn’t true. Heads-Tails actually has a 50% chance, while Heads-Heads and Tails-Tails each have a 25% chance. There are several ways to see why.
One is simply counting the combinations. Each coin can either be heads or tails. So the combinations are:
|Coin 1||Coin 2||Total|
Heads-Tails happens 2 out of 4 times, which is 50%.
Another way to see this is to flip one coin, then flip the other one. If the first coin is Heads, then the second coin can either be Heads (resulting in Heads-Heads) or Tails (resulting in Heads-Tails). Tails-Tails is obviously impossible since one coin is already Heads.
The logic also applies if the first coin is Tails. The second coin can either be Heads (Heads-Tails) or Tails (Tails-Tails). Heads-Heads is impossible.
No matter what the first coin flip is, you always have a 50% chance of getting Heads-Tails. But in order to get Heads-Heads you need both the first coin and the second coin to be Heads.
This fact has a surprisingly large amount of implications. For example, if you’re having kids and want one boy and one girl this is good news, you have a solid 50% chance at it.
In football it means in a 2-game series you’re most likely going to go 1-1. In other sports with 7 game series the road team will have a good chance of picking up at least one win on the road in those first 2 games.