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%.
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!
Can you determine the probability that one OR the other event will occur, using the information given?
the chance of rain or snow tomorrow, given that P (shower) = 10% and P (storm) = 1%
The likelihood that you left your keys in your pocket or your backpack,
given that P(pocket)=10% and P(backpack)=80%
The probability that a child has at least one curly-haired parent, given that the probability of curly hair in a population is 30%