1. 12.4 Probability of Compound Events
Algebra 2

2. Probabilities of Unions and Intersections
Union of A and B: all the outcome of two events A and B
Intersection of A and B: Only the outcomes shared by both A and B
Compound Events: The union or intersection of two events
Mutually exclusive events: When no outcomes are shared by A and B.

3. Probability of Compound Events
If A and B are two events, then the probability of A or B is:
P(A or B) = P(A) + P(B) – P(A and B)
If A and B are mutually exclusive, then the probability of A or B is:
P(A or B) = P(A) + P(B)

4. Examples:
One six-sided die is rolled. What is the probability of rolling a multiple of 3 or 5
One six-sided die is rolled. What is the probability of rolling a multiple of 3 or a multiple of 2?

5. Example:
In a poll of high school juniors, 6 out of 15 took a French class and 11 out of 15 took a math class. Fourteen out of 15 students took French or math. What is the probability that a student took both French and math?

6. Examples:
In a survey of 200 pet owners, 103 owned dogs, 88 owned cats, 25 owned birds, and 18 owned reptiles.
None of the respondents owned both a cat and a bird. What is the probability that they owned a cat or a bird?
Of the respondents, 52 owned both a cat and a dog. What is the probability that a respondent owned a cat or a dog?

7. Example continue:
In a survey of 200 pet owners, 103 owned dogs, 88 owned cats, 25 owned birds, and 18 owned reptiles.
Of the respondents, 119 owned a dog or a reptile. What is the probability that they owned a dog and a reptile?

8. Using Complements
Complement: consists of all outcomes that are not in event A (called A’)
Probability Of The Complement Of An Event
The probability of the complement of A is P(A’) = 1 – P(A)

9. Example:
A card is randomly selected from a standard deck of 52 cards. Find the probability of the given event.
The card is not a king.
The card is not an ace or a jack.

10. Example:
One high school requires students to complete 30 hours of community service to graduate. There are 156 different community service options to choose from. What is the probability that in a group of 5 students, at least 2 of them will be doing the same service.

11. Example:
Seven prizes are being given in a raffle contest tickets are sold. After each prize is called, the winning ticket is returned to the drawing box and is eligible to be picked for anther prize. What is the probability that at least one of the tickets is drawn twice?