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4.4 Mutually Exclusive Events

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Mutually Exclusive Events

Mutually exclusive (disjoint) events

Addition rule for mutually exclusive events:
P(A∪B)=P(A)+P(B)P(A \cup B) = P(A) + P(B)
Extension: For n{n} mutually exclusive events:
P(A1∪A2∪⋯∪An)=P(A1)+P(A2)+⋯+P(An)P(A_1 \cup A_2 \cup \cdots \cup A_n) = P(A_1) + P(A_2) + \cdots + P(A_n)

Examples of mutually exclusive events:

  • Roll a die: getting a 3 and getting a 5 (can't happen simultaneously)
  • Draw a card: getting a heart and getting a spade

Examples of NOT mutually exclusive:

  • Drawing a card that is red OR a face card (King of Hearts is both!)
  • Being a female student OR being in AP Stats (could be both)

Check: Are A and B mutually exclusive? → Can they both occur at the same time?

In this unit

12 lessons

  1. 4.1Introducing Statistics: Random and Non-Random Patterns?Preview lesson
  2. 4.2Estimating Probabilities Using SimulationPreview lesson
  3. 4.3Introduction to ProbabilityPreview lesson
  4. 4.4Mutually Exclusive EventsThis lesson
  5. 4.5Conditional ProbabilityPreview lesson
  6. 4.6Independent Events and Unions of EventsPreview lesson
  7. 4.7Introduction to Random Variables and Probability DistributionsPreview lesson
  8. 4.8Mean and Standard Deviation of Random VariablesPreview lesson
  9. 4.9Combining Random VariablesPreview lesson
  10. 4.10Introduction to the Binomial DistributionPreview lesson
  11. 4.11Parameters for a Binomial DistributionPreview lesson
  12. 4.12The Geometric DistributionPreview lesson

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