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.