Some fine prints relating to the Law of OR
Once again, the Law of OR says, if you need to know the probability that one thing OR another will take place, just add their separate probabilities.
Of course its not (quite) that simple. Here’s the fine print: the events in question have to be mutually exclusive. That means they cannot happen together. In Life’s a Game, you will win one prize, but not two, or three, or four.
Here are some mutually exclusive events:
- Your friend is pregnant OR not pregnant; as we all know, there’s no such thing as a little pregnant.
- Your mother offers you cake OR a brownie for dessert. You can’t get both!
- You have one dollar. You can buy fries OR a donut OR a small milkshake, but after you buy one thing, your money’s gone, you’re out of luck.
Here are some non-mutually exclusive events:
- Your grandmother offers you cake OR a brownie OR both. (Taking both is a different outcome to taking just one).
- Your friend has a cold OR a flu OR maybe both, (You could get unlucky and get both).
- You just got paid, to celebrate you could get fries OR a donut OR a small milkshake OR any combination of the above.
For each of these, does it describe mutually exclusive choices?
The chance of a shower or a storm in the forecast tomorrow?
You think you left your keys in your pocket or your backpack?
The chance that a curly-haired child has a father OR a mother with curly hair?