Transcript 2.8 - probability and odds

Chapter 2 – Properties of
Real Numbers
2.8 – Probability and Odds
2.8 – Probability and Odds
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Today we will be learning about:
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Finding the probability of an event
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Finding the odds of an event
2.8 – Probability and Odds
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Probability of an event – measure of the
likelihood that the event will occur.
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It is a number between 0 and 1
2.8 – Probability and Odds
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Outcomes – different possible results
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When an event has N equally likely outcomes,
each of them occur with probability 1/N.
Example: Rolling a six-sided number cube, the
possible outcomes are 1, 2, 3, 4, 5, and 6. The
probability associated with each outcome is 1/6.
2.8 – Probability and Odds
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EVENT – all of the possible outcomes
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THEORETICAL PROBABILITY - the
probability that should happen.
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In the roll of a six-sided number cube, an “even
roll” consists of the outcomes 2, 4, and 6.
The theoretical probability of an even roll is 3/6 =
½.
FAVORABLE OUTCOMES – the outcomes
you wish to have happen.
2.8 – Probability and Odds
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Theoretical Probability P =
Number of favorable outcomes
Total number of outcomes
2.8 – Probability and Odds
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Another type of probability is
EXPERIMENTAL PROBABILITY. This
type of probability is based on repetitions of an
actual experiment and is calculated by the
following rule.
Experimental probability P =
Number of favorable outcomes observed
Total number of trials
2.8 – Probability and Odds
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Example 1
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You have 2 red and 2 black socks in a drawer.
You reach in and pick two without looking. What
is the probability P that they do not match
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In a group of students, 12 ride the bus to school, 8
are driven to school, and 5 walk. One of the
students is chosen at random from the group.
What is the probability P that the student walks to
school?
2.8 – Probability and Odds
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Example 2
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Use the circle graph below showing the responses of 250
college students to a survey asking “Which factor is most
likely to influence your job choice after graduation?” If
you were to ask a randomly chosen college student this
question, what is the experimental probability that the
student would say “type of company?”
Salary93
location103
Type of
company
37
Size of
company
17
2.8 – Probability and Odds
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THE ODDS OF AN EVENT
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When all outcomes are equally likely, the ODDS
that an event will occur are given by the formula:
ODDS = Number of favorable outcomes
Number of unfavorable outcomes
2.8 – Probability and Odds
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Example 3
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You randomly choose a letter from the word
SUMMER. What are the odds that the letter is a
vowel?
2.8 – Probability and Odds
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Example 4
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The probability that a randomly chosen 4 digit
security code contains at least one zero is 0.34.
What are the odds that a 4 digit security code
contains at least one zero?
2.8 – Probability and Odds
HOMEWORK
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