Mutually exclusive events
Events that cannot happen at the same time. For these, you add their probabilities, and the probabilities of all outcomes add to 1.
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Analogy
Like a traffic light: it cannot be red and green at once.
Example
P(red or blue) = 5/10 + 3/10 = 8/10P(not green) = 1 - 2/10 = 8/10
In practice
If the chance of rain is 0.3, the chance of no rain is 0.7.
Practice
Flashcards
- If P(rain) = 0.3, what is P(no rain)?0.7, since probabilities add to 1.
Questions people ask
What does P(not A) equal?
It equals 1 - P(A). Either the event happens or it does not, so the two probabilities add to 1. If P(rain) is 0.3, then P(no rain) is 1 - 0.3 = 0.7. It is often the quickest route. It is useful whenever counting the chances of the event not happening is easier than counting it happening.
When do you add probabilities?
Add when you want the chance of one event OR another and they cannot both happen. For one dice roll, P(1 or 2) = 1/6 + 1/6 = 2/6. If the events can overlap, adding gives too much. For overlapping events, subtract the overlap once, or you will count those outcomes twice.