Mathematics 4 Life and Beyond: Sample Spaces (11-3)

Sample Spaces

Vocabulary

Sample Space- all the possible outcomes of an experiment.

Fundamental Counting Principal- state that you can find the total number of outcomes for two or more experiments by multiplying the number of outcomes for each separate experiment.

Examples

In probability theory, the sample space ^[^nb ¹^] of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually denoted using set notation, and the possible outcomes are listed as elements in the set.

SampleSpaces

Unit 6 > Lesson 3 of 12

Experiment 1:

What is the probability of each outcome when a dime is tossed?

Outcomes:

The outcomes of this experiment are head and tail.

Probabilities:

P(head)	=	1
		2

P(tail)	=	1
		2

Definition: The sample space of an experiment is the set of all possible outcomes of that experiment.

The sample space of Experiment 1 is: {head, tail}

Experiment 2:

A spinner has 4 equal sectors colored yellow, blue, green and red. What is the probability of landing on each color after spinning

this spinner?

Sample Space:

{yellow, blue, green, red}

Probabilities:

P(yellow)	=	1
		4

P(blue)	=	1
		4

P(green)	=	1
		4

P(red)	=	1
		4

Experiment 3:

What is the probability of each outcome when a single

6-sided die is rolled?

Sample

Space:

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

Probabilities:

P(1)	=	1
		6

P(2)	=	1
		6

P(3)	=	1
		6

P(4)	=	1
		6

P(5)	=	1
		6

P(6)	=	1
		6

Experiment 4:

A glass jar contains 1 red, 3 green, 2 blue and 4 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of each outcome?

Sample Space:

{red, green, blue, yellow}

Probabilities:

P(red)	=	1
		10

P(green)	=	3
		10

P(blue)	=	2	=	1
		10		5

P(yellow)	=	4	=	2
		10		5

Summary:

The sample

space of an experiment is the set of all possible outcomes for that experiment. You may have noticed that for each of the experiments above, the sum of the probabilities of each outcome is 1. This is no coincidence. The sum of the probabilities of the distinct outcomes within a sample space is 1.

The sample space for choosing a single card at random from a deck of 52 playing

cards is shown below. There are 52 possible outcomes in this sample space.