Probability

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Probability
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Learning Goal

• I will be able to calculate the probability of an
  event.

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Basic Definitions
Outcome result of an experiment Sample Space
all possible outcomes Event subset of
sample space
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Sample Space

• Find the sample space for tossing three coins.
• HHH
• HHT
• HTH
• HTT
• THH
• THT
• TTH
• TTT

There should be 8 outcomes in the sample space.
We know, because each coin has two possible
outcomes, so 2 2 2.
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Probability
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Key Concepts
And independent multiply Or mutually
exclusive add Limitations of Probability
Complement of an event all outcomes not in the
event P(complement) 1 P(event)
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Probability Example
Find the probability of seeing three heads when
three coins are tossed.
Event 3 heads Outcomes HHH P(3 heads) 1/8
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Probability Example
In the Texas Lotto, a player chooses six
different numbers from 1 to 54. If these six
numbers match the six numbers drawn by the
lottery commission, the player wins. What is the
probability of winning, if the player buys one
ticket?
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Probability Example

• In 2001, approximately 65 of the population of
  the United States was 25 years old or older. In
  a survey, 10 people were chosen at random from
  the population. What is the probability that all
  10 were 25 years or older?

Each person is independent of the others. So,
since each person has a probability of 0.65 of
being 25 years or older, multiply all those
0.65s together.
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Probability Example
13 cards are dealt from a standard 52-card deck.
What is the probability of dealing at least one
heart?
P(at least one heart) 1 P(no hearts)
0.987
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Learning Goal

• I will be able to calculate the probability of an
  event.

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End of notes.

• Do Gateway problem on worksheet.
• If successful, homework is 1 5 8 13.
• If not successful, homework is 1 13.