# Addition rule for "OR"

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##### Examples
###### Lessons
1. Mutually Exclusive VS. Not Mutually Exclusive
Consider the experiment of rolling a die.
1. Event A: an even number is thrown
Event B: an odd number is thrown
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 events A, B mutually exclusive?
iii) Determine the following probabilities:
$\cdot$ P(A)
$\cdot$ P(B)
$\cdot$ P(A or B)
$\cdot$ P(A and B)
2. Event A: an even number is thrown
Event B: a multiple of three is thrown
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 events A, B mutually exclusive?
iii) Determine the following probabilities:
$\cdot$ P(A)
$\cdot$ P(B)
$\cdot$ P(A or B)
$\cdot$ P(A and B)
3. Supplementary info on mutually exclusive and addition rule.
2. 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
1. using the formula.
2. using the Venn Diagram.
3. A card is drawn from a standard deck of 52 cards. Determine the probability that:
1. a heart or a spade is drawn.
2. a heart or a face card is drawn.
3. an ace or a face card is drawn.
4. an ace or a spade is drawn.
4. Use the following information to determine whether the events A, B are mutually exclusive.
1. $P(A)=0.5$
$P(B)=0.3$
$P(A\;$or$\;B)=0.7$
2. $P(A)=\frac{2}{3}$
$P(B)=\frac{1}{5}$
$P(A\;$or$\;B)=\frac{13}{15}$
3. $P(A)=\frac{7}{12}$
$P(B)=\frac{5}{13}$
$P(A\;$and$\;B)=0$
###### Topic Notes
$\cdot$ 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)