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Use of probability to describe uncertainty

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1. Key Ideas. Use of probability to describe uncertainty. How probability is determined ... Among 30 people, the chance of a matching birthday is greater that 70 ... – PowerPoint PPT presentation

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Title: Use of probability to describe uncertainty


1
Lesson 8a
The Language of Probability
  • Use of probability to describe uncertainty
  • How probability is determined
  • Probability examples

Key Ideas
1
2
  • 1. Uncertainty is Part of Decision Making in
    Science
  • Can we be certain that a new wheat variety will
    yield more than an old one?
  • What are the chances that a new therapy will
    cause side-effects?
  • If a new environmental regulation is put in
    place, will it have the desired effect?

2
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  • 2. Probability is a Numerical Measure of
    Uncertainty.
  • The chance that it will rain is 30 or the
    probability is .30.
  • A new therapy will work on 60 of the population,
    or the probability it will work is .60.
  • The chance that the harvest will set a new record
    is 50-50, or the probability is .50.

3
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  • 3. Some Properties of Probability
  • Probability is a value between 0 and 1.
  • An event that has probability near 0 is unlikely
    to occur.
  • An event that has probability near 1 is very
    likely to occur.

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5
?
  • 4. How Do We Obtain Probability?
  • Logical reasoning
  • coin toss, lotteries, etc.
  • Empirically (Take data)
  • chance of rain, chance of product failure
  • Subjectively
  • Chance that your favorite team will win next game

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  • Example 1. Toss a coin 3 times. What is the
    probability of getting exactly 2 heads?
  • List outcomes so that all are equally likely to
    occur.
  • Possibilities 1 2 3 4 5 6 7 8
  • Toss 1 H H H T H T T T Toss
    2 H H T H T H T T
  • Toss 3 H T H H T T H T
  • Of the 8 possibilities, 3 have exactly 2 heads,
    so the probability is 3/8 .375.

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  • Example 2. The birthday problem.
  • Suppose we ask each person in a group of 30 to
    give his or her day of birth, e.g. Oct 10, Sept.
    15, etc.
  • Do you think it is likely or unlikely that there
    would be 2 people among a group of 30 that would
    have the same birthday?
  • How big a group would we have to have for there
    to be a 50-50 chance that 2 birthdays among the
    group match?

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  • Example 2 (continued). Caution We are not
    asking what is the chance that two people are
    born on a given day such as Jan. 10, rather what
    is the chance that there is a matching birthday,
    whatever the day may be.
  • Among 30 people, the chance of a matching
    birthday is greater that 70.
  • With 50 people, the chance is about 97.
  • With 23 people, the chance is about 50.

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Is it easy or hard to figure the probability of
winning a lottery or a game of chance?
The idea is simple enough. List the possible
outcomes so that all are equally likely to occur.
Figure the proportion that are winners. The
difficulty is in counting the possibilities.
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