# Addition rule for "OR"

##### Intros

##### Examples

###### Lessons

**Mutually Exclusive VS. Not Mutually Exclusive**

Consider the experiment of rolling a die.- Event
: an even number is thrown**A**

Event: an odd number is thrown**B**

i) List the outcomes for:

$\cdot$ event**A**

$\cdot$ event**B**

$\cdot$ event**A****or****B**

$\cdot$ event**A****and****B**

ii) Mark the outcomes on the Venn Diagram. Are eventsmutually exclusive?**A, B**

iii) Determine the following probabilities:

$\cdot$ P()**A**

$\cdot$ P()**B**

$\cdot$ P(**A****or**)**B**

$\cdot$ P(**A****and**)**B**

- Event
: an even number is thrown**A**

Event: a multiple of three is thrown**B**

i) List the outcomes for:

$\cdot$ event**A**

$\cdot$ event**B**

$\cdot$ event**A****or****B**

$\cdot$ event**A****and****B**

ii) Mark the outcomes on the Venn Diagram. Are eventsmutually exclusive?**A, B**

iii) Determine the following probabilities:

$\cdot$ P()**A**

$\cdot$ P()**B**

$\cdot$ P(**A****or**)**B**

$\cdot$ P(**A****and**)**B**

- Supplementary info on mutually exclusive and addition rule.

- Event
- There are 20 students in a class. 9 students like pizza and 7 students like pasta. Of these students, 3 students like both. Determine the probability that a randomly selected student in the class like pizza or pasta
- A card is drawn from a standard deck of 52 cards. Determine the probability that:
- Use the following information to determine whether the events
are mutually exclusive.*A, B*

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###### Topic Notes

$\cdot$ P(

$\cdot$ If events

- events

- in the Venn Diagram, the circle for

- P(

$\cdot$ If events

- events

- in the Venn Diagram, the circle for

- P(

*or***A***): probability of event***B***occurring or event***A***occurring***B****during a single trial**.$\cdot$ If events

*are mutually exclusive:***A, B**- events

*have no common outcomes.***A, B**- in the Venn Diagram, the circle for

*and the circle for***A***have no area of overlap.***B**- P(

*or***A***) = P(***B***) + P(***A***)***B**$\cdot$ If events

*are not mutually exclusive:***A, B**- events

*have common outcomes.***A, B**- in the Venn Diagram, the circle for

*and the circle for***A***have an area of overlap representing the event***B***and***"A***.***B"**- P(

*or***A***) = P(***B***) + P(***A***) – P(***B***and***A***)***B**2

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