# 5: What if you violate the fine print?

Prize

Chances

Washer-dryer

5%

Toaster Oven

10%

Tropical Getaway

1%

Pet Rocks

84%

Here is the original table of probabilities. You can see that the chance
of winning a major prize (washer-dryer, toaster, or getaway) = 16%.

Let’s say we want to figure out the chance that you will win an appliance
OR a major prize.

If you blindly apply the Law of OR, you would write:

P(major prize OR appliance) = P(major prize) + P(appliance)
= 16% + 15% = 31%.

Pretty good odds! But don’t get too excited yet. The problem is that we “double-counted”,
because your chances of winning the toaster or the washer-dryer both got counted
twice! Really, your chances should be:

P(major prize OR appliance) = P(getaway OR appliance) = 1%
+ 15% = 16%.

In
fact, there is a rule that allows you to correct for the effect of double-counting,
but we’re not going to go into it here — and in any case, you can only use
it if you know how much double-counting is happening.

In general, though, if two events are not mutually exclusive, you
can’t add the probabilities to figure out the probability of one event
or the other.
Sorry!