1. 12-7 Probability of Compound Events (AND problems)
Goal:
Find the probability of a compound event.
Eligible Content: A

2. Vocabulary
Independent Events – the outcome of one event does not affect the outcome of another event.
Probability of picking a red marble, replacing it, and then picking a green marble from a bag.
Dependent Events – the outcome of one event affects the outcome of another event.
Probability of picking a red marble, NOT replacing it, and then picking a green marble from a bag.

3. Independent Events Multiply the probabilities together.
P(A and B) = P(A) * P(B)

4. Dependent Events
Multiply the probabilities together, but be careful when finding second probability. You have to decrease the total amount!!
P(A and B) = P(A) * P(B)

5. Example #1
A bag of marbles contains 4 black, 8 blue, 6 yellow and 5 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. Independent P(black, yellow) = 0.05

6. Example #2
At a carnival, winners in the ring-toss game are randomly given a prize from a bag that contains 4 sunglasses, 6 hairbrushes, and 5 key chains. Two prizes are randomly drawn from the bag and not replaced. Find the probability of selecting a hairbrush then sunglasses. Dependent P(hairbrush, sunglasses) = 0.11

7. Example #3
A toy bin contains 6 stuffed animals, 4 dolls, 8 puzzles and 2 books. What is the probability of randomly selecting a stuffed animal, replacing it in bin, then selecting a doll? Independent P(stuffed animal, doll) = 0.06

8. Example #4
A toy bin contains 6 stuffed animals, 4 dolls, 8 puzzles and 2 books. What is the probability of randomly selecting a puzzle, then selecting a book without replacing the first toy? Dependent P(puzzle, book) = 0.04

9. Example #5
There are 12 books on a table. There are 5 math books, 2 biology books, 4 social studies books, and 1 Spanish book. What is the probability of randomly selecting a math book, returning it to the table, then selecting a biology book? Independent P(math, biology) = 0.07

10. Example #6
There is a candy dish on the table. In the dish there are 5 Snickers bars, 2 Kit Kats, 4 Reese’s peanut butter cups, and 7 Milky Way bars. What is the probability of randomly selecting a Snickers bar, eating it, then selecting a Milky Way bar? Dependent P(Snickers, Milky Way) = 0.11

11. A gumball machine contains 16 red gumballs, 10 blue gumballs, and 18 green gumballs. Once a gumball is removed from the machine, it is not replaced.
Find: P(red, green, blue)
A. 0.03
B. 0.04
C. 0.05
D. 0.06

12. A gumball machine contains 16 red gumballs, 10 blue gumballs, and 18 green gumballs. Once a gumball is removed from the machine, it is replaced.
Find: P(green, blue)
A. 0.09
B. 0.64
C. 0.10
D. 0.16

13. Practice
Page 797 #1-4

14. Homework
Pages #11,13,14
#19-23