Lesson 3.1 Terminology

Experiment

An experiment is a planned operation carried out under controlled conditions. In a chance experiment, the results are not predetermined.

Example: Roll one fair six-sided die and observe the face that is showing.

Example: Draw one card from a regular 52-card deck (a regular 52 card deck has 13 hearts, 13 clubs, 13 spades, and 13 diamonds).

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Outcome

An outcome is a result of an experiment.

Example: One outcome of rolling a fair six-sided die is a {1} (the face of the die showing is a 1).

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A sample space is all possible outcomes of an experiment.

Example: All possible outcomes for rolling a fair six-sided die are {1, 2, 3, 4, 5, 6}.

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Event

An event is any combination of outcomes. Upper case letters are used for events.

Example:

Let event A = rolling a face greater than 1 (rolling a 2, 3, 4, or 5) when you roll one fair six-sided die.

Let event B = rolling an odd-numbered face (rolling a 1, 3, or 5) when you roll one fair six-sided die.

Probability

The probability of any outcome of an experiment is the long-term relative frequency of that outcome. Recall that relative frequency is the fraction of times an answer occurs.

Example: All possible outcomes for rolling a fair six-sided die are

{1, 2, 3, 4, 5, 6}.

Each of these outcomes is equally likely. If we rolled the die 600 times, we would expect 100 faces that showed a 1. The long-term relative frequency or probability of rolling a 1 is 1/6. If event A = rolling a 1, then we write P(A) = 1/6.

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Equally Likely

Each outcome has an equal chance of happening.

Example: All possible outcomes for rolling a fair six-sided die are {1, 2, 3, 4, 5, 6}. Each outcome is equally likely.

If we rolled the die 600 times, we would expect 100 faces that showed a 1, 100 that showed a 2, 100 that showed a 3, 100 that showed a 4, 100 that showed a 5, and 100 that showed a 6.

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A OR B

A OR B means that an outcome is in event A OR is event B OR in events A and B at the same time.

Example: All possible outcomes for rolling a fair six-sided die are {1, 2, 3, 4, 5, 6}.

Let A = rolling a 2, 3, or 4.

Let B = rolling a 4 or 5.

A OR B = {2, 3, 4, 5}

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A AND B

A AND B means that an outcome is in both eventsA AND B at the same time

Example: All possible outcomes for rolling a fair six-sided die are {1, 2, 3, 4, 5, 6}.

Let A = rolling a 2, 3, or 4

Let B =rolling a 4 or 5

A AND B = {4} (4 is in both A and B)

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Complement

The complement of event A, A' (read "A prime"), are all outcomes in the sample space that are not in A.

Example: All possible outcomes for rolling a fair six-sided die are {1, 2, 3, 4, 5, 6}. Suppose A = {1, 2, 3, 5}. Then A' = {4, 6}.

P(A) + P(A') = 4/6 + 2/6 = 1.

In general, P(Event) + P(Complement of Event) = 1.

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Conditional Probability

The conditional probability of A knowing that B has already occurred is written as P(A|B). Calculate the probabilty of A from the sample space of B.

Example: All possible outcomes for rolling a fair six-sided die are {1, 2, 3, 4, 5, 6}. Suppose B = {1, 3, 5, 6} and A = {1, 3}. P(A | B) = 2/4.

The formula to calculate P(A | B) is:

P(A | B) = P(A AND B) / P(B)

(Divide P(A AND B) by P(B))

To do the previous example using the formula, remember that the sample space is {1, 2, 3, 4, 5, 6}, A = {1, 3} and B = {1, 3, 5, 6}.

Notice that P(A AND B) = 2/6 (There are 2 outcomes that are both in A and B). P(B) = 4/6.

P(A AND B) / P(B) = (2/6) / (4/6) = 2/4.

This example shows how to find probabilities from a sample space.

Please continue to the next section of this lesson.

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