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

$\cdot$ If events**A, B** are mutually exclusive:

- events**A, B** have no common outcomes.

- in the Venn Diagram, the circle for**A** and the circle for **B** have no area of overlap.

- P(**A** or **B**) = P(**A**) + P(**B**)

$\cdot$ If events**A, B** are not mutually exclusive:

- events**A, B** have common outcomes.

- in the Venn Diagram, the circle for**A** and the circle for **B** have an area of overlap representing the event **“A** and **B”**.

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

$\cdot$ If events

- events

- in the Venn Diagram, the circle for

- P(

$\cdot$ If events

- events

- in the Venn Diagram, the circle for

- P(

- 1.
- 2.
**Mutually Exclusive VS. Not Mutually Exclusive**

Consider the experiment of rolling a die.a)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**

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**c)Supplementary info on mutually exclusive and addition rule. - 3.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 pastaa)using the formula.b)using the Venn Diagram.
- 4.A card is drawn from a standard deck of 52 cards. Determine the probability that:a)a heart or a spade is drawn.b)a heart or a face card is drawn.c)an ace or a face card is drawn.d)an ace or a spade is drawn.
- 5.Use the following information to determine whether the events
are mutually exclusive.*A, B*a)$P(A)=0.5$ $P(B)=0.3$ $P(A\;$or$\;B)=0.7$b)$P(A)=\frac{2}{3}$ $P(B)=\frac{1}{5}$ $P(A\;$or$\;B)=\frac{13}{15}$c)$P(A)=\frac{7}{12}$ $P(B)=\frac{5}{13}$ $P(A\;$and$\;B)=0$

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