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Probability Definitions Help

By — McGraw-Hill Professional
Updated on Oct 25, 2011

Probability Definitions—Event Versus Outcome

Here are definitions of some common terms that will help us understand what we are talking about when we refer to probability.

Event Versus Outcome

The terms event and outcome are easily confused. An event is a single occurrence or trial in the course of an experiment. An outcome is the result of an event.

If you toss a coin 100 times, there are 100 separate events. Each event is a single toss of the coin. If you throw a pair of dice simultaneously 50 times, each act of throwing the pair is an event, so there are 50 events.

Suppose, in the process of tossing coins, you assign “heads” a value of 1 and “tails” a value of 0. Then when you toss a coin and it comes up “heads,” you can say that the outcome of that event is 1. If you throw a pair of dice and get a sum total of 7, then the outcome of that event is 7.

The outcome of an event depends on the nature of the hardware and processes involved in the experiment. The use of a pair of “weighted” dice usually produces different outcomes, for an identical set of events, than a pair of “unweighted” dice. The outcome of an event also depends on how the event is defined. There is a difference between saying that the sum is 7 in a toss of two dice, as compared with saying that one of the die comes up 2 while the other one comes up 5.

Sample Space

A sample space is the set of all possible outcomes in the course of an experiment. Even if the number of events is small, a sample space can be large.

Table 8-1 The sample space for an experiment in which a coin is tossed four times. There are 16 possible outcomes; “heads” = 1 and “tails” = 0.

Event 1

Event 2

Event 3

Event 4

0

0

0

0

0

0

0

1

0

0

1

0

0

0

1

1

0

1

0

0

0

1

0

1

0

1

1

0

0

1

1

1

1

0

0

0

1

0

0

1

1

0

1

0

1

0

1

1

1

1

0

0

1

1

0

1

1

1

1

0

1

1

1

1

If you toss a coin four times, there are 16 possible outcomes. These are listed in Table 8-1 , where “heads” = 1 and “tails” = 0. (If the coin happens to land on its edge, you disregard that result and toss it again.)

If a pair of dice, one red and one blue, is tossed once, there are 36 possible outcomes in the sample space, as shown in Table 8-2. The outcomes are denoted as ordered pairs, with the face-number of the red die listed first and the face-number of the blue die listed second.

Table 8-2 The sample space for an experiment consisting of a single event, in which a pair of dice (one red, one blue) is tossed once. There are 36 possible outcomes, shown as ordered pairs (red, blue).

Red → Blue ↓

1

2

3

4

5

6

1

(1,1)

(2,1)

(3,1)

(4,1)

(5,1)

(6,1)

2

(1,2)

(2,2)

(3,2)

(4,2)

(5,2)

(6,2)

3

(1,3)

(2,3)

(3,3)

(4,3)

(5,3)

(6,3)

4

(1,4)

(2,4)

(3,4)

(4,4)

(5,4)

(6,4)

5

(1,5)

(2,5)

(3,5)

(4,5)

(5,5)

(6,5)

6

(1,6)

(2,6)

(3,6)

(4,6)

(5,6)

(6,6)

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