Download File 1 basic and compound probability

10-1 Probability
Warm Up
Problem of the Day
Lesson Presentation
Course 3
Warm Up
Multiply. Write each fraction in simplest form.
1. 2  3
5
5
6
25
2. 1 + 3
6
6
2
3
Write each fraction as a decimal.
2
3.
5
0.4
32
4.
125
0.256
Warm-Up
1. Reduce 12/15 to
lowest terms
2. Change 2 ¾ to an
improper fraction
3.
Fraction
Decimal
Percent
8/25
5.25
3%
10-1 Probability
Each observation of an experiment is called a
trial, and each result is called an outcome.
The sample space is the set of all possible
outcomes of an experiment.
Experiment
Sample Space
flipping a coin ----
heads, tails
rolling a number cube --
1, 2, 3, 4, 5, 6
guessing the number of
marbles in a jar
---
whole numbers
Course 3
10-1 Probability
•The probability of an event occurring can
written as a decimal, fraction, or percent.
• A probability of 0 means the event is impossible, or
can never happen.
• A probability of 1 or 100% means the event is
certain, or has to happen.
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10-1 Probability
Never
happens
0
0
0%
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Happens about
half the time
1
4
0.25
25%
Always
happens
1
2
3
4
1
0.5
0.75
1
50%
75%
100%
10-1 Probability
The probabilities of all of the
outcomes in a sample space must
add up to 1 or 100%.
Course 3
10-1 Probability
Give the probability for each outcome.
The basketball team has a
70% chance of winning.
The probability of winning is P(win) = 70% = 0.7.
The probabilities must add to 1 or 100%, so the probability
of not winning, P(lose) = 1 – 0.7 = 0.3, or 30%.
Course 3
10-1 Probability
Give the probability for each outcome.
The polo team has a
60% chance of
winning.
The probability of winning is P(win) = 60% = 0.6.
The probabilities must add to 1 or 100%, so the probability
of not winning, P(lose) = 1 – 0.6 = 0.4 or 40%.
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10-1 Probability
Probability, when written as a fraction:
Outcome you are looking for
All possible outcomes
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10-1 Probability
What is the probability of each outcome?
Rolling a number cube.
Outcome
1
2
3
4
5
6
Probability
1 1 1 1 1 1
+ + + + + =1 
6 6 6 6 6 6
Check The probabilities of all the outcomes must add to 1.
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10-1 Probability
Give the probability for each outcome.
3 3
2
+ +
=1 
8 8
8
Check The probabilities of all the outcomes
must add to 1.
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10-1 Probability
When finding the probability of one event OR
the other, you simply add the probabilities
together.
Course 3
10-1 Probability
A quiz contains 5 true/false questions. Suppose you guess
randomly on every question. The table below gives the
probability of each score.
What is the probability of guessing 1 or more correct?
The event “one or more correct” consists of the outcomes 1, 2, 3, 4, or 5.
P(1 or more correct) = 0.156 + 0.313 + 0.313 + 0.156 + 0.031 =
0.969 or 96.9%
Course 3
10-1 Probability
A quiz contains 5 true or false questions. Suppose you guess
randomly on every question. The table below gives the probability
of each score.
What is the probability of guessing fewer than 3 correct?
The event “fewer than 3” consists of the outcomes 0, 1, or 2.
P(fewer than 3) = 0.031 + 0.156 + 0.313 = 0.5 or 50%
Course 3
10-1 Probability
A quiz contains 5 true or false questions. Suppose you guess
randomly on every question. The table below gives the
probability of each score.
What is the probability of guessing fewer than 2 correct?
The event “fewer than 2 correct” consists of the outcomes 0 or 1.
P(fewer than 2 correct) = 0.031 + 0.156
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= 0.187 or 18.7%
10-1 Probability
A quiz contains 5 true or false questions. Suppose you guess
randomly on every question. The table below gives the probability
of each score.
What is the probability of guessing 2 or more correct?
The event “two or more correct” consists of the outcomes 2, 3, 4, or 5.
P(2 or more) = 0.313 + 0.313 + 0.156 + 0.031 = .813 or 81.3%.
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Vocabulary
A compound event is made up of one or
more separate events.
P(event, event) is the same as P(event and event)
And (in probability) means to multiply.
Three separate boxes each have one blue
marble and one green marble. One marble is
chosen from each box.
What is the probability of choosing a blue marble from
each box? P (blue, blue, blue)
1
.
2
P(blue, blue, blue) = 1 · 1
2
2
In each box, P(blue) =
Multiply.
·
1 = 1 = 0.125
2
8
Three separate boxes each have one blue
marble and one green marble. One marble is
chosen from each box.
What is the probability of choosing a blue marble, then a green
marble, and then a blue marble?
In each box, P(blue) = 1 .
2
In each box, P(green) = 1 .
2
P(blue, green, blue) = 1
2
·
1
2
Multiply.
·
1 = 1 = 0.125
2
8
10-1 Probability
Insert Lesson Title Here
Lesson Quiz
Use the table to find the probability of each
event.
1. P(1 or 2)
2. P(not 3)
3. P(2, 3, or 4)
4. P(1 and 5)
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0.351
0.874
0.794
0.004368
Closing
• What do you do when you see the word
AND in probability?
• What do you do when you see the word
OR in probability?
• What do you do when you see the word
NOT in probability?
10-1 Probability
Six students are in a race. Ken’s
probability of winning is 0.2. Lee is
twice as likely to win as Ken. Roy is 1
4
as likely to win as Lee. Tracy, James,
and Kadeem all have the same
chance of winning. Create a table of
probabilities for the sample space.
Course 3
10-1 Probability
1
Understand the Problem
The answer will be a table of probabilities.
Each probability will be a number from 0 to
1. The probabilities of all outcomes add to 1.
List the important information:
• P(Ken) = 0.2
• P(Lee) = 2  P(Ken) = 2  0.2 = 0.4
1 
1
• P(Roy) = 4 P(Lee) = 4 0.4 = 0.1
• P(Tracy) = P(James) = P(Kadeem)
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10-1 Probability
2
Make a Plan
You know the probabilities add to 1, so
use the strategy write an equation. Let
p represent the probability for Tracy,
James, and Kadeem.
P(Ken) + P(Lee) + P(Roy) + P(Tracy) + P(James) + P(Kadeem) = 1
0.2 + 0.4
+ 0.1
+
p
+
p
+
p
=1
0.7 + 3p = 1
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10-1 Probability
4
Look Back
Check that the probabilities add to 1.
0.6 + 0.2 + 0.1 + 0.1 = 1 
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