Sullivan Algebra and Trigonometry: Section 14.3

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Sullivan Algebra and Trigonometry Section 14.3

• Objectives of this Section
• Construct Probability Models
• Compute Probabilities of Equally Likely Outcomes
• Utilize the Addition Rule to Find Probabilities
• Compute Probabilities Using Permutations and
  Combinations

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An event is an outcome from an experiment.
The probability of an event is a measure of the
likelihood of its occurrence.
A probability model lists the different outcomes
from an experiment and their corresponding
probabilities.
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To construct probability models, we need to know
the sample space of the experiment. This is the
set S that lists all the possible outcomes of the
experiment.
Determine the sample space resulting from the
experiment of rolling a die.
S 1, 2, 3, 4, 5, 6
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The probability of each outcome in the sample
space S e1, e2, , en has two properties
The probability assigned to each outcome is
non-negative and at most 1.
The sum of all probabilities equals 1.
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Probability for Equally Likely Outcomes
If an experiment has n equally likely outcomes,
and if the number of ways an event E can occur is
m, then the probability of E is
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A classroom contains 20 students 7 Freshman, 5
Sophomores, 6 Juniors, and 2 Seniors. A student
is selected at random. Construct a probability
model for this experiment.
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Theorem Additive Rule
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What is the probability of selecting an Ace or
King from a standard deck of cards?
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Probabilities of Complementary Events If E
represents any event and represents the
complement of E, then
Suppose the probability that a hurricane hits a
county in a given year is 0.02. Find the
probability that a hurricane doesnt hit the
county.
Since there are only two possible events in the
sample space, hurricane or no hurricane, these
events are complementary.
Prob(No H) 1 - Prob(H) 1 - 0.02 0.98
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Suppose you managed a little league team. You
have 8 pitchers, 10 fielders, and 5 other players
on the bench. If you choose three players at
random, what is the probability that they are all
pitchers?
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