12-7 Probability of Compound Events (AND problems)

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Presentation transcript:

12-7 Probability of Compound Events (AND problems) Goal: Find the probability of a compound event. Eligible Content: A1.2.3.3.1

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.

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

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)

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

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

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

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

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

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

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

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

Practice Page 797 #1-4

Homework Pages 797-798 #11,13,14 #19-23