Transcript independent events

Independent
Independentand
andDependent
10-7Events
10-7
Dependent Events
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Algebra
Holt
Algebra
11
Independent and Dependent
10-7 Events
Warm Up
Find the theoretical probability of each
outcome
1. rolling a 6 on a number cube.
2. rolling an odd number on a number cube.
3. flipping two coins and both landing head
up
Holt Algebra 1
Independent and Dependent
10-7 Events
Objectives
Find the probability of independent
events.
Find the probability of dependent
events.
Holt Algebra 1
Independent and Dependent
10-7 Events
Vocabulary
independent events
dependent events
Holt Algebra 1
Independent and Dependent
10-7 Events
Adam’s teacher gives the class two list of titles and
asks each student to choose two of them to read.
Adam can choose one title from each list or two
titles from the same list.
Holt Algebra 1
Independent and Dependent
10-7 Events
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.
Holt Algebra 1
Independent and Dependent
10-7 Events
Example 1: 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.
Dependent; your friend cannot pick the card you
picked and has fewer cards to choose from.
B. You flip a coin and it lands heads up. You flip
the same coin and it lands heads up again.
Independent; the result of the first toss does not
affect the sample space for the second toss.
Holt Algebra 1
Independent and Dependent
10-7 Events
Check It Out! Example 1
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.
Independent; the result of rolling the number
cube the 1st time does not affect the result of the
2nd roll.
b. One student in your class is chosen for a
project. Then another student in the class
is chosen.
Dependent; choosing the 1st student leaves fewer
students to choose from the 2nd time.
Holt Algebra 1
Independent and Dependent
10-7 Events
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.
Holt Algebra 1
Independent and Dependent
10-7 Events
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.
To determine the probability of two independent
events, multiply the probabilities of the two
events.
Holt Algebra 1
Independent and Dependent
10-7 Events
Holt Algebra 1
Independent and Dependent
10-7 Events
Example 2A: 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?
Because the first marble is replaced after it is
selected, the sample space for each selection is the
same. The events are independent.
Holt Algebra 1
Independent and Dependent
10-7 Events
Example 2A Continued
P(red, green) = P(red)  P(green)
The probability of selecting red
is
, and the probability of
selecting green is
Holt Algebra 1
.
Independent and Dependent
10-7 Events
Example 2B: Finding the Probability of Independent
Events
A coin is flipped 4 times. What is the
probability of flipping 4 heads in a row.
Because each flip of the coin has an equal
probability of landing heads up, or a tails, the
sample space for each flip is the same. The events
are independent.
P(h, h, h, h) = P(h) • P(h) • P(h) • P(h)
The probability of landing
heads up is with
each event.
Holt Algebra 1
Independent and Dependent
10-7 Events
Check It Out! Example 2
An experiment consists of spinning the
spinner twice. What is the probability of
spinning two odd numbers?
The result of one spin does
not affect any following
spins. The events are
independent.
With 6 numbers on the spinner, 3 of which are
odd, the probability of landing on two odd
numbers is
.
P(odd, odd) = P(odd) • P(odd)
Holt Algebra 1
Independent and Dependent
10-7 Events
Lesson Quiz: Part I
Tell whether each set of events is independent or
dependent. Explain your answer.
1. flipping two different coins and each coin
landing showing heads
Independent; the flip of the first coin does not
affect the sample space for the flip of the second
coin.
2. drawing a red card from a standard deck of cards
and not replacing it; then drawing a black card
from the same deck of cards
Dependent; there are fewer cards to choose
from when drawing the black card.
Holt Algebra 1
Independent and Dependent
10-7 Events
Lesson Quiz: Part II
3. 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?
4. 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?
Holt Algebra 1
Independent and Dependent
10-7 Events
Lesson Quiz: Part III
5. A number cube is rolled two times. What is
the probability of rolling an even number first
and then a number less than 3?
Holt Algebra 1