Applications of Addition Rule

Mutually Exclusive Events

Lesson Objective:

• IDENTIFY MUTUALLY EXCLUSIVE EVENTS

• Use Addition Rules of Probability

• CALCULATE PROBABILITIES

​Vocabulary

Mutually Exclusive Events

When two events CANNOT happen at the same time, the events are said to be MUTUALLY EXCLUSIVE.

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An example of this is getting heads on a coin and a tail on the same coin in the same toss.

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Another example would be getting a six on a regular die and a five on the same die in the same roll.

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A pre-Covid example would be being at school and being at home at the same time.

ADDITION RULE for MUTUALLY EXCLUSIVE EVENTS

ADDITION RULE for NON-MUTUALLY EXCLUSIVE EVENTS

More complicated OR

• To the right you see cards that can each be described in two ways

• Jack, Queen, King or Ace

• Heart, Club, Diamond or Spade

• So, one card can be two things at once, for example a Queen and a Heart.

When we talk about OR probabilities we have to take "double identity" into account.

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P(Queen or Heart) seems simple... just add the Queen probability to the Heart probability.... BUT

What about the Queen of Hearts? It will get counted twice, so....

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We will have to consider OR and take away AND to get rid of the double count

​ In this simple example we can count the cards shown to see this is true!

​Mutually Exclusively

Solution

​Overlapping Events