Download Reteaching 9-1

4/8/13
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Reteaching 9-1
Probability
To find a theoretical probability, first list all
possible outcomes. Then use the formula:
number of favorable outcomes
P(event) = total
number of possible outcomes
A letter is selected at random from the letters
of the word FLORIDA. What is the probability
that the letter is an A?
Selecting a letter other than A is called not A
and is the complement of the event A. The sum
of the probabilities of an event and its
complement equals 1, or 100%.
What is the probability of the event “not A”?
P(A) P(not A) 1
1
7
• There are 7 letters (possible outcomes).
P(not A) 1
6
1
P(not A) 1 7 7
• There is one A, which represents a
favorable outcome.
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The probability of the event “not A”
of favorable outcomes
1
P(A) number
total number of outcomes = 7
(selecting F, L, O, R, I, or D) is 67.
The probability that the letter is an A is 17.
Spin the spinner shown once. Find each probability as a fraction,
a decimal, and a percent.
1. P(5)
5
2. P(odd number)
number of favorable outcomes
total number of outcomes
7
2
number of favorable outcomes
total number of outcomes
8
10
=
5
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2
=
You select a card at random from a box that contains cards numbered
from 1 to 10. Find each probability as a fraction, a decimal, and a percent.
3. P(even number)
4. P(number less than 4)
5. P(not 5)
The letters H, A, P, P, I, N, E, S, and S are written on pieces of paper.
Select one piece of paper. Find each probability.
6. P(not vowel)
7. P(not E)
A number is selected at random from the numbers 1 to 50. Find the
odds in favor of each outcome.
8. selecting a multiple of 5
Course 2 Lesson 9-1
9. selecting a factor of 50
Reteaching
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Reteaching 9-2
Experimental Probability
Probability measures how likely it is that an event will occur. For an
experimental probability, you collect data through observations or
experiments and use the data to state the probability.
G
B G
R
R B
G
G
B
R
B
B
R
G R
G
B B
G
The jar contains red, green, and blue chips. You shake the jar, draw a
chip, note its color, and then put it back. You do this 20 times with
these results: 7 blue chips, 5 red chips, and 8 green chips. The
experimental probability of drawing a green chip is
P(green chip) =
number of times “green chips” occur
total number of trials
G
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8 = 2 = 0.4 = 40%
P(green chip) = 20
5
The probability of drawing a green chip is 25, or 0.4, or 40%.
Sometimes a model, or simulation, is used to represent a situation.
Then, the simulaton is used to find the experimental probability.
For example, spinning this spinner can simulate the probability that
1 of 3 people is chosen for president of the student body.
1. What is the experimental probability
of drawing a red chip? Write the
probability as a fraction.
P(red chip) =
20
2. What is the experimental probability
of drawing a blue chip? Write the
probability as a percent.
=
P(blue chip) =
=
Suppose you have a bag with 30 chips: 12 red, 8 white, and 10 blue.
You shake the jar, draw a chip, note its color, and then put it back.
You do this 30 times with these results: 10 blue chips, 12 red chips,
and 8 white chips. Write each probability as fraction in simplest form.
3. P(red)
4. P(white)
5. P(blue)
Describe a probability simulation for each situation.
6. You guess the answers on a true/false
test with 20 questions.
Course 2 Lesson 9-2
7. One student out of 6 is randomly chosen
to be the homeroom representative.
Reteaching
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Use the 20 draws above to complete each exercise.
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Reteaching 9-3
Sample Spaces
The set of all possible outcomes of an experiment is called the sample space.
You can use a tree diagram or a table to show
the sample space for an experiment. The tree
diagram below shows the sample space for
spinning the spinner and tossing a coin.
H
1
3
2
Evelyn and Kara are planning to go skating or
to a movie. Afterward they want to go out for
pizza, tacos, or cheeseburgers. How many
possible choices do they have?
T
H
2
T
H
• There are two choices for an activity and
three choices for food.
T
• First choices ⫻ Second choices
3
H
T
2
There are 6 possible outcomes: 1H, 1T, 2H, 2T,
3H, 3T. What is the probability of spinning a 3
and tossing heads? There is one favorable
outcome (3H) out of 6 possible outcomes. The
probabilty is 16.
⫻
3
=6
There are 6 possible choices.
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1
Complete the tree diagram to show the sample space.
1. Roll a number cube and toss a coin. What is the probability of
getting (4, Heads)?
1
2
3
4
5
6
Number of outcomes
P(4, heads) =
Use the counting principle to find the number of possible outcomes.
2. 4 kinds of yogurt and 8 toppings
3. 6 shirts and 9 pairs of slacks
4. 3 types of sandwiches and 3 flavors
5. 4 types of bread and 6 different
of juice
Course 2 Lesson 9-3
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You can use the counting principle to find the
number of possible outcomes: If there are
m ways of making one choice and n ways of
making a second choice, then there are
m ⫻ n ways of making the first choice followed
by the second.
sandwich spreads
Reteaching
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Reteaching 9-4
If you toss a coin and roll a number cube,
the events are independent. The outcome
of one event does not affect the outcome of
the second event.
Find the probability of tossing a heads (H) and
rolling an even number (E).
Find P(H and E). H and E are independent.
1
Compound Events
If the outcome of the first event affects
the outcome of the second event, the
events are dependent.
A bag contains 3 blue and 3 red marbles. Draw
a marble, then draw a second marble without
replacing the first marble. Find the probability
of drawing 2 blue marbles.
1
Find P(H):
3 blue 5 1
P(blue) = 6 marbles
2
s
1
P(H) = 12 head
sides 5 2
2
2
Find P(E):
Find P(blue after blue).
2 blue 5 2
P(blue after blue) = 5 marbles
5
1
P(E) = 36 evens
faces 5 2
3
Find P(blue).
P(H and E) = P(H) ⫻ P(E) = 12 3 12 5 14
3
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Find P(blue, then blue)
P(blue, then blue)
= P(blue) ⫻ P(blue after blue)
In Exercises 1–3, you draw a marble at random from the bag of marbles
shown. Then, you replace it and draw again. Find each probability.
1. P(blue, then red)
2. P(2 reds)
3. P(2 blues)
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5 12 3 25 5 15
B R
R R B
R
R R B
B
Next, you draw two marbles randomly without replacing the first
marble. Find each probability.
4. P(blue, then red)
5. P(2 reds)
6. P(2 blues)
You draw two letters randomly from a box containing the letters
M, I, S, S, O, U, R, and I.
7. Suppose you do not replace the first letter before drawing the
second. What is P(M, then I)?
8. Suppose you replace the first letter before drawing the second.
What is P(M, then I)?
Course 2 Lesson 9-4
Reteaching
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Reteaching 9-5
Step 1
Date
Simulating Compound Events
Choose a simulation tool.
• You can use a number cube when there are 6 equally
likely outcomes.
• You can use a spinner with x number of equal spaces
when there are x equally likely outcomes.
• You can use a coin when there are 2 equally likely
outcomes.
• You can use random digits.
Step 2
Decide which outcomes are favorable.
Step 3
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• Choose what you need to land on, roll, or toss to get a
favorable outcome.
Describe a trial.
• For each trial, use your simulation tool until you get a
favorable outcome.
• Record the number of times you use your tool to get
your favorable outcome.
Step 4
Perform 20 trials. Then estimate the probability.
One-fourth of the students in the seventh grade have no siblings. Design a simulation for estimating
the probability that you would need to ask at least two students before finding one with no siblings.
1. Choose a simulation tool.
2. Decide which outcomes are favorable.
Course 2 Lesson 9-5
Reteaching
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• Make a table showing your 20 trials and their outcomes.
• Use that to find the probability: the number of
favorable outcomes over 20.
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Reteaching 9-5 (continued)
Simulating Compound Events
3. Describe a trial.
4. Perform 20 trials.
Students Asked to Find One with No Siblings
Frequency
2
5. Find the probability that you would need to ask at least two
students before finding one with no siblings.
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1
Reteaching
Course 2 Lesson 9-5