Sample Space Topic Index | Algebra Index | Regents Exam Prep Center

A sample space is a set of all possible outcomes
for an activity or experiment.

 Activity Sample Space Rolling a die There will be 6 outcomes in the sample space: {1, 2, 3, 4, 5, 6} Tossing a coin There will be 2 outcomes in the sample space: { Heads, Tails} Drawing a card from a standard deck There will be 52 cards in the sample space: {Spades: 2,3,4,5,6,7,8,9,10, ace, jack queen, king, Clubs:  2,3,4,5,6,7,8,9,10, ace, jack, queen, king, Diamonds:  2,3,4,5,6,7,8,9,10, ace, jack, queen, king, Hearts:  2,3,4,5,6,7,8,9,10, ace, jack, queen, king} Drawing one marble from the bottle There will be 8 marbles in the sample space: {blue marble, blue marble, blue marble, blue marble, blue marble, red marble, red marble, red marble} Rolling a pair of dice There will be 36 outcomes in the sample space: {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)   (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)   (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)   (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)   (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)     (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)} Choosing an outfit from a green blouse, a red blouse, a black skirt, a pair of sneakers, and a pair of sandals There will be 4 outfit combinations in the sample space: {green blouse-skirt-sneakers, green blouse-skirt-sandals, red blouse-skirt-sneakers, red blouse-skirt-sandals}

As you can see, sample spaces can become very large.

When determining a sample space, be sure to consider ALL possibilities.  Oftentimes this can be a difficult task.  To make this process easier, we may wish to use the Counting Principle.

 Remember:  A sample space is the set of ALL possible outcomes.

 Topic Index | Algebra Index | Regents Exam Prep Center Created by Donna Roberts