# 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-dyer, 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 probabilities are not mutually exclusive, you
can't add them, which means you can't 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 (rain) = 10% and P (snow) = 1%

(To make this problem interactive, turn on javascript!)

- I need a hint ... : the chances of rain and snow are not mutually exclusive

- ...another hint ... : it could be both

#### I think I have the answer: we can't say anything

### the likelihood that you left your keys

in your pocket or your backpack,

given that P(pocket)=10% and P(backpack)=80%

(To make this problem interactive, turn on javascript!)

- I need a hint ... : keys can be in one place, so we can use the Law of OR to get P (in pocket OR in backpack)
- ...another hint ... : 10% + 80%

#### I think I have the answer: 10% + 80% = 90%

### the probability that your father or your mother has curly hair,

given that the probability of curly hair in a population is 30%

(To make this problem interactive, turn on javascript!)

- I need a hint ... : its possible that both of your parents could have curly hair
- ...another hint ... : these options are not mutually exclusive

#### I think I have the answer: we can't say anything

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