Download Algebra 1

Warm Up
• Find the theoretical probability of each
outcome
1. rolling a 4 on a number cube.
2. rolling an even number on a number cube.
3. flipping two coins and both landing tails up
Monday, December 19, 2016
• Warm-up
• Dependent vs Independent Events
• Practice
• Homework: Due Wednesday: Pg. 731: 1-35,
odds
Algebra 1
Independent and Dependent Event
Objectives
• Find the probability of independent events.
• Find the probability of dependent events.
Definitions
• Events are independent events if the
occurrence of one event does not affect the
probability of the other. Events are dependent
events if the occurrence of one event does
affect the probability of the other.
Classifying Events as
Independent or Dependent
• Tell whether each set of events is
independent or dependent. Explain you
answer.
A. You select a card from a standard deck of
cards and hold it. A friend selects another
card from the same deck.
B. You flip a coin and it lands heads up. You flip
the same coin and it lands heads up again.
Check It Out!
• Tell whether each set of events is
independent or dependent. Explain you
answer.
a. A number cube lands showing an odd
number. It is rolled a second time and lands
showing a 6.
b. One student in your class is chosen for a
project. Then another student in the class is
chosen.
Tree Diagram
• Suppose an experiment involves flipping two
fair coins. The sample space of outcomes is
shown by the tree diagram. Determine the
theoretical probability of both coins landing
heads up.
Independent Probabilities
• Now look back at the separate theoretical
probabilities of each coin landing heads up.
The theoretical probability in each case is .
The product of these two probabilities is
the same probability shown by the tree
diagram.
•
Independent Probabilities
Finding the Probability of
Independent Events
• An experiment consists of randomly selecting
a marble from a bag, replacing it, and then
selecting another marble. The bag contains 3
red marbles and 12 green marbles. What is
the probability of selecting a red marble and
then a green marble?
Example
• A coin is flipped 4 times. What is the
probability of flipping 4 heads in a row.
Check It Out!
• An experiment consists of spinning the
spinner twice. What is the probability of
spinning two odd numbers?
Dependent Probabilities
• Suppose an experiment involves drawing
marbles from a bag. Determine the theoretical
probability of drawing a red marble and then
drawing a second red marble without
replacing the first one.
Dependent Probabilities
• To determine the probability of two
dependent events, multiply the probability of
the first event times the probability of the
second event after the first event has
occurred.
Application
• A snack cart has 6 bags of pretzels and 10
bags of chips. Grant selects a bag at random,
and then Iris selects a bag at random. What is
the probability that Grant will select a bag of
pretzels and Iris will select a bag of chips?
Check It Out!
• A bag has 10 red marbles, 12 white marbles,
and 8 blue marbles. Two marbles are
randomly drawn from the bag. What is the
probability of drawing a blue marble and
then a red marble?
Warm-Up
1. Eight cards are numbered from 1 to 8 and placed
in a box. One card is selected at random and not
replaced. Another card is randomly selected.
What is the probability that both cards are
greater than 5?
2. An experiment consists of randomly selecting a
marble from a bag, replacing it, and then
selecting another marble. The bag contains 3
yellow marbles and 2 white marbles. What is the
probability of selecting a white marble and then a
yellow marble?`