1. Probability of Compound Events

2. Compound Events Made up of two or more events.
Example: the probability that a flight will be on time & your luggage will arrive.
Create your own compound event.

3. Independent Events
The outcome of one event does NOT affect the outcome of the other.
Equation: P(A and B) = P(A) x P(B)
Symbol A n B
Example 1 : A bag contains 6 black marbles, 9 blue marbles, 4 yellow marbles, and 2 green marbles. A marble is selected, replaced, and a second marble is selected. Find the probability of selecting a black marble, then a yellow marble.

4. Example 2: P(blue, green)
Example 3: P(not black, blue)

5. Dependent Events
The outcome of one event affects the outcome of another event.
Equation: P(A and B) = P(A) x P(B following A)
Example 4 : A bag contains 6 black marbles, 9 blue marbles, 4 yellow marbles, and 2 green marbles. A marble is selected, then a second marble is selected. Find the probability of selecting a black marble, then a yellow marble.

6. Example 5: P(blue, green)
Example 6: P(not black or blue, blue)

7. Complement of a Set
The set of all objects that do NOT belong to the given set.
Example: The probability of drawing a heart & the probability of NOT drawing a heart.
Create your own complement.
The sum of these probabilities is ALWAYS 1 whole or 100%.

8. CARDS Total number of cards in a deck? ______
How many suits? _____ Name them.
How many cards are in each suit? _____
How many cards of each face? _____
How many different face cards? Name them.
How many of each color? _____

9. Mutually Exclusive Events
Events that can NOT occur at the same time.
Example: the probability of drawing a heart or a diamond.
Equation: P(A or B) = P(A) + P(B)
Symbol A u B
Example 7: A die is being rolled. Find the probability of rolling a 3 or 5.

10. Example 8: P(at least 4)
Example 9: P(less than 3)

11. Not Mutually Exclusive
Events that CAN occur at the same time.
Example: the probability of being on the honor roll, in the SADD club, or being both on the honor roll & in the club.
Equation: P(A or B) = P(A) + P(B) – P(A and B)

12. Example 10: Of 240 girls, 176 are on the Honor Roll, 48 play sports, and 36 are on the Honor Roll and play sports. What is the probability that a randomly selected student plays sports or is on the Honor Roll?
Example 11: Out of 5200 households surveyed, 2107 had a dog, had a cat, and 303 had both a dog and a cat. What is the probability that a randomly selected household has a dog or a cat?

13. Review
Draw a model to describe the following terms. Define each: Mutually Exclusive, Independent, Compound Events, Not Mutually Exclusive, & Dependent.

14. Circle the sample space
What is the proportion of students who live in Currituck & are male?
What is the probability that a male student who passes Math II is also in the SADD Club?

15. Name three different probability models…