Holt Algebra 1 10-7 Independent and Dependent Events Warm Up Find the theoretical probability of...
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Holt Algebra 1 10-7 Independent and Dependent 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
Holt Algebra 1 10-7 Independent and Dependent Events Warm Up Find the theoretical probability of each outcome 1. rolling a 6 on a number cube. 2. rolling
Slide 11. 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
Independent and Dependent 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 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
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
Example 2: Try It Now
a. A number cube lands showing an odd number. It is rolled a second
time and lands showing a 6.
Tell whether each set of events is independent or dependent.
Explain you answer.
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 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
To determine the probability of two independent events, multiply
the probabilities of the two 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.
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
P(red, green) = P(red) P(green)
The probability of selecting red is , and the probability of
selecting green is .
Holt Algebra 1
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
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.
.
Independent and Dependent 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
draw
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.
Holt Algebra 1
Independent and Dependent 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
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 Events
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.
P(pretzel and chip) = P(pretzel) P(chip after pretzel)
•
The probability that Grant selects a bag of pretzels and Iris
selects a bag of chips is .
Holt Algebra 1
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 Events
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.
P(blue and red) = P(blue) P(red after blue)
•