Transcript Compound Probability ppt

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
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:
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
Example 2: Try It Now
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 3:
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 3 (cont)
P(red, green) = P(red)  P(green)
The probability of selecting red
is
, and the probability of
selecting green is
Holt Algebra 1
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Independent and Dependent
10-7 Events
Example 4:
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
Example 5: Try It Now
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
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 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 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 Algebra 1
Independent and Dependent
10-7 Events
Example 6:
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 Algebra 1
Independent and Dependent
10-7 Events
P(pretzel and chip) = P(pretzel) • P(chip after pretzel)
Grant selects one of 6 bags of
pretzels from 16 total bags.
Then Iris selects one of 10
bags of chips from 15 total
bags.
The probability that Grant selects a bag of
pretzels and Iris selects a bag of chips is .
Holt Algebra 1
Independent and Dependent
10-7 Events
Example 7: Try It Now
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 Algebra 1
Independent and Dependent
10-7 Events
P(blue and red) = P(blue) • P(red after blue)
One of 8 blue marbles is
selected from a total of 30
marbles. Then one of 10 red
marbles is selected from the
29 remaining marbles.
The probability that first a blue marble is
selected and then a red marble is selected is
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