§4.1–Probability Basics
Tom Lewis
Fall Term 2009
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
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Outline
1
Introduction
2
Frequency and probability
3
Basic properties of probabilities
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
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Introduction
Problem
Toss a fair coin 3 times in succession and record the outcomes (H or T).
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
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Introduction
Problem
Toss a fair coin 3 times in succession and record the outcomes (H or T).
Use a tree diagram to list the outcomes of this experiment.
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
3/6
Introduction
Problem
Toss a fair coin 3 times in succession and record the outcomes (H or T).
Use a tree diagram to list the outcomes of this experiment.
What probability should be assigned to each outcome?
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
3/6
Introduction
Problem
Toss a fair coin 3 times in succession and record the outcomes (H or T).
Use a tree diagram to list the outcomes of this experiment.
What probability should be assigned to each outcome?
What is the probability of tossing exactly 2 heads?
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
3/6
Introduction
Problem
Toss a fair coin 3 times in succession and record the outcomes (H or T).
Use a tree diagram to list the outcomes of this experiment.
What probability should be assigned to each outcome?
What is the probability of tossing exactly 2 heads?
What is the probability of tossing at least 2 heads.
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
3/6
Introduction
Problem
Toss two dice (red and black)
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
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Introduction
Problem
Toss two dice (red and black)
What is the probability that the sum of the faces is 9?
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
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Introduction
Problem
Toss two dice (red and black)
What is the probability that the sum of the faces is 9?
What is the probability that the outcome of the red die is strictly
greater than the outcome of the black die?
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
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Frequency and probability
Frequency
Consider a probability experiment and let E be an outcome of this
experiment.
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
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Frequency and probability
Frequency
Consider a probability experiment and let E be an outcome of this
experiment.
Repeat this experiment N times.
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
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Frequency and probability
Frequency
Consider a probability experiment and let E be an outcome of this
experiment.
Repeat this experiment N times.
Let #E count the number of times that E has occurred in the N
trials.
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
5/6
Frequency and probability
Frequency
Consider a probability experiment and let E be an outcome of this
experiment.
Repeat this experiment N times.
Let #E count the number of times that E has occurred in the N
trials.
#E
As N → ∞,
→ probability of E . In other words, the frequency
N
with which E occurs tends to the probability of E as the number of
trials increases without bound.
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
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Basic properties of probabilities
Basic properties of probabilities
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Basic properties of probabilities
Basic properties of probabilities
1
The probability of an event is always between 0 and 1.
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
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Basic properties of probabilities
Basic properties of probabilities
1
The probability of an event is always between 0 and 1.
2
The probability of an event that cannot occur is 0.
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
6/6
Basic properties of probabilities
Basic properties of probabilities
1
The probability of an event is always between 0 and 1.
2
The probability of an event that cannot occur is 0.
3
The probability of an event that must occur is 1.
Tom Lewis ()
§4.1–Probability Basics
Fall Term 2009
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