Transcript Holt McDougal Algebra 1 10-7

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 McDougal Algebra 1
Independent and Dependent
10-7 Events
Objectives
Find the probability of independent
events.
Find the probability of dependent
events.
Holt McDougal 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 McDougal 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 McDougal 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 McDougal 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 McDougal 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 McDougal 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 McDougal Algebra 1
Independent and Dependent
10-7 Events
Holt McDougal 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 McDougal 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 McDougal 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 McDougal Algebra 1
Independent and Dependent
10-7 Events
Check It Out! Example 2a
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 McDougal Algebra 1
Independent and Dependent
10-7 Events
Check It Out! Example 2b
An experiment consists of randomly selecting a
marble from a bag, replacing it, and then
selecting another marble. The bag contains 3
red marbles, 5 blue marbles, and 7 green
marbles. What is the probability of selecting a
red marble and then a green marble?
Holt McDougal Algebra 1
Independent and Dependent
10-7 Events
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.
Probability of drawing a red marble on the first draw
Holt McDougal Algebra 1
Independent and Dependent
10-7 Events
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.
Probability of drawing a red marble on the second
draw
Holt McDougal Algebra 1
Independent and Dependent
10-7 Events
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.
Holt McDougal Algebra 1
Independent and Dependent
10-7 Events
Example 3A: 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?
Holt McDougal Algebra 1
Independent and Dependent
10-7 Events
Example 3B: Application
Joy and Tony are both picking puppies
from a litter of Labrador retrievers. There
are 2 black labs, 3 yellow labs, and 1
chocolate lab. If Joy selects a puppy at
random, and then Tony selects a puppy at
random. What is the probability that both
will select a black lab?
Holt McDougal Algebra 1
Independent and Dependent
10-7 Events
Check It Out! Example 3a
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?
Holt McDougal Algebra 1
Independent and Dependent
10-7 Events
Check It Out! Example 3b
In a standard deck of 52 playing cards
there are four kings. A card is drawn at
random from the deck, and then a
second card is drawn at random. What
is the probability that both cards are
kings?
Holt McDougal Algebra 1