Probability

Probability&Statistics

Study Guides

Big Picture

Probability is the study of whether an event will or will not occur. Using the laws of probability, we can find the likelihood

of two events occurring together, not occurring, or a large variety of other combinations.

Key Terms

Probability: A measure of how likely an event is.

Complementary Event: All the other events in a

Event: Something that occurs. Can have one or more

sample space.

possible outcomes.

Compound Event: An event made up of two or more

Simple Event: An event that has exactly one outcome.

simple events.

Sample Space: All the possible outcomes of a

Dependent Events: Events whose outcomes do affect

experiment.

each other.

Outcome: The result of a single experiment.

Independent Events: Events whose outcomes don’t

Experiment: The process of taking a measurement or

affect each other.

making an observation.

Determining Probabilities

The probability of an event can be calculated by knowing the number of ways the event can occur and the size of

the sample space.

•

Probability of event A = P(A) =

•

Probability of an event is always between 0 and 1: 0 = impossible, 1 = always happens

The probabilities of all possible outcomes of an event must add up to 1. This means one of the outcomes must happen.

This method of determining probabilities assumes that all the possible outcomes are equally likely to happen.

Simple Events

Example: the probability that a die will land on 3

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Experiment: rolling a single die

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Event: the die lands on 3

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This is also a simple event because the die can only land on one number (one possible outcome)

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Sample space S lists the possible outcomes: S = {1, 2, 3, 4, 5, 6}

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Size of sample space = six

•

P(die lands on 3) =

Non-Simple Events

Example: the probability that a die will land on either 2 or 3

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Event: the die lands on 2 or 3

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Can be broken down to two simple events: the die lands on 2, the die lands on 3

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Sample space S = {1, 2, 3, 4, 5, 6}

•

Size of sample space = six

•

P(die lands on 2 or 3) =

•

There are two ways for the event to happen – the die can land on 2 or the die can land on 3

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Complementary Events

Complement of an event A = A’ = all the events other than A in the sample space

Finding probabilities using complements:

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P(A’) = probability that A doesn’t happen

Example: Throwing a die

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Event A = observing an odd number, Event A’ = observing an even number

The Complement Rule:

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P(A) + P(A’) = 1

•

can be rearranged: P(A’) = 1–P(A)

•

The Complement Rule is useful when P(A’) is easier to find than P(A)

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This guide was created by Lizhi Fan and Jin Yu. To learn more about the student

authors, visit http://www.ck12.org/about/about-us/team/interns.

v1.1.9.2012