SECTION 4.1 BASIC IDEAS Copyright 2014 The McGraw-Hill
Companies, Inc. Permission required for reproduction or
display.
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Objectives 1. Construct sample spaces 2. Compute and interpret
probabilities 3. Approximate probabilities using the Empirical
Method Copyright 2014 The McGraw-Hill Companies, Inc. Permission
required for reproduction or display.
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Construct sample spaces Objective 1 Copyright 2014 The
McGraw-Hill Companies, Inc. Permission required for reproduction or
display.
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Probability Experiment A probability experiment is one in which
we do not know what any individual outcome will be, but we do know
how a long series of repetitions will come out. For example, if we
toss a fair coin, we do not know what the outcome of a single toss
will be, but we do know what the outcome of a long series of tosses
will be about half heads and half tails. Copyright 2014 The
McGraw-Hill Companies, Inc. Permission required for reproduction or
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Probability The probability of an event is the proportion of
times that the event occurs in the long run. So, for a fair coin,
that is, one that is equally likely to come up heads as tails, the
probability of heads is 1/2 and the probability of tails is 1/2.
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Law of Large Numbers The law of large numbers says that as a
probability experiment is repeated again and again, the proportion
of times that a given event occurs will approach its probability.
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Sample Space The collection of all the possible outcomes of a
probability experiment is called a sample space. Example: Suppose
that a coin is tossed. The sample space consists of: {Heads, Tails}
Suppose that a standard die is rolled. The sample space consists
of: {1, 2, 3, 4, 5, 6} Copyright 2014 The McGraw-Hill Companies,
Inc. Permission required for reproduction or display.
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Event We are often concerned with occurrences that consist of
several outcomes. For example, when rolling a die, we might be
concerned with the possibility of rolling an odd number. A
collection of outcomes of a sample space is called an event.
Example: A probability experiment consists of rolling a die. The
sample space is {1, 2, 3, 4, 5, 6}. The event of rolling an odd
number = {1, 3, 5}. Copyright 2014 The McGraw-Hill Companies, Inc.
Permission required for reproduction or display.
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Probability Model Once we have a sample space for an
experiment, we need to specify the probability of each event. This
is done with a probability model. We use the letter P to denote
probabilities. For example, if we toss a coin, we denote the
probability that the coin lands heads by P(Heads). Notation: If A
denotes an event, the probability of event A is denoted by P(A).
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Probabilities With Equally Likely Outcomes If a sample space
has n equally likely outcomes, and an event A has k outcomes, then
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Compute and interpret probabilities Objective 2 Copyright 2014
The McGraw-Hill Companies, Inc. Permission required for
reproduction or display.
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Example A fair die is rolled. Find the probability that an odd
number comes up. Solution: The sample space has six equally likely
outcomes: {1, 2, 3, 4, 5, 6} The event of an odd number has three
outcomes: {1, 3, 5} The probability is: Copyright 2014 The
McGraw-Hill Companies, Inc. Permission required for reproduction or
display.
