Sample space
The sample space is the complete set of all possible outcomes for a probability experiment, listed in curly braces. Grade 6 Saxon Math Course 1 students identify sample spaces as the essential first step before calculating any probability. Rolling a six-sided die gives {1, 2, 3, 4, 5, 6}; flipping a coin gives {Heads, Tails}. For combined experiments, the Fundamental Counting Principle says to multiply outcome counts: a die roll and coin flip together produce 6 × 2 = 12 equally likely outcomes.
Key Concepts
Property The set of possible outcomes for an event is called the sample space.
Examples Rolling a standard number cube: Sample space = \{1, 2, 3, 4, 5, 6\}.
Explanation Before you can find the probability of anything, you need to know all the things that could happen. The sample space is just a fancy list of every single possible result. Are you flipping a coin? The sample space is just {Heads, Tails}. It's your map of the entire 'world' of possibilities for that one experiment.
Common Questions
What is a sample space?
The set of all possible outcomes for an experiment, listed in curly braces. Example: {1, 2, 3, 4, 5, 6} for one die roll.
What is the sample space for flipping two coins?
{HH, HT, TH, TT} — four possible outcomes.
How many outcomes for rolling a die and flipping a coin?
6 × 2 = 12, by the Fundamental Counting Principle.
Why must you know the sample space before finding probability?
Probability = favorable outcomes ÷ total outcomes. Without the complete sample space you cannot determine the denominator.
Does the order of listing outcomes in a sample space matter?
No. What matters is that every distinct possible outcome is included exactly once.