Sample Space Statistics Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
List the sample space for rolling a standard six-sided die and flipping a coin simultaneously.

Solution

  1. 1
    Step 1: The die has outcomes {1, 2, 3, 4, 5, 6} and the coin has outcomes {H, T}.
  2. 2
    Step 2: The sample space is all possible combinations: pair each die outcome with each coin outcome.
  3. 3
    Step 3: S={(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)}S = \{(1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (4,T), (5,H), (5,T), (6,H), (6,T)\}. Total outcomes: 6×2=126 \times 2 = 12.

Answer

The sample space has 12 outcomes: {(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)}\{(1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (4,T), (5,H), (5,T), (6,H), (6,T)\}.
The sample space is the set of all possible outcomes of an experiment. For combined experiments, the total number of outcomes equals the product of the individual outcome counts (multiplication principle). Listing the sample space systematically ensures no outcomes are missed.

About Sample Space

The sample space is the complete set of all possible outcomes for a probability experiment, listed without repetition. It forms the foundation for every probability calculation because the probability of any event is a fraction of the sample space.

Learn more about Sample Space →

More Sample Space Examples

Example 2 medium

A restaurant offers 3 starters (soup, salad, bread), 4 mains (chicken, fish, beef, pasta), and 2 des

Example 3 medium

A password consists of one letter (A–E) followed by one digit (1–3). (a) List the entire sample spac

Example 4 hard

Two dice are rolled. (a) How many outcomes are in the sample space? (b) How many outcomes give a sum

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