13.6 Notes- Probability of Mutually Exclusive Events

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Vocab To Know

Mutually Exclusive- two events that cannot happen at the same time

Complements- all the outcomes in a sample space that are not included

Mutually Exclusive

Like a Venn diagram, each event is one circle. Mutually exclusive events don't touch, non-mutually exclusive events do. Remember: and means multiply, or means add. Also remember to subtract double counting when dealing with non-mutually exclusive events! If the answer is greater than 1, you've double counted.

Drawing an ace or queen in a deck of cards IS mutually exclusive, because you can't draw an ace and queen at the same time.

Drawing an ace or spades in a deck of cards IS NOT mutually exclusive, because you can draw and ace of spades.

ex. Probability of rolling a 3 or 4 on a die...

1/6 + 1/6 = 2/6 or 1/3

ex. Probability of rolling evens or greater than 2 on a die...

1/2 + 2/3 - 1/3 = 5/6

Complements

The formula is: 1 - (probability of event) = (complement)

ex. There is a 70% chance it will rain

Complement: 30%