Sample Space Math Example 2

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

Example 2

medium
Two coins are flipped. Write out the sample space, assign probabilities to each outcome, and find P(exactly one head)P(\text{exactly one head}).

Solution

  1. 1
    List all outcomes: S={HH,HT,TH,TT}S = \{HH, HT, TH, TT\}, so ∣S∣=4|S| = 4
  2. 2
    Each equally likely: P(each)=14P(\text{each}) = \frac{1}{4}; verify sum: 4×14=14 \times \frac{1}{4} = 1 ✓
  3. 3
    Identify favorable outcomes for exactly one head: {HT,TH}\{HT, TH\} — two outcomes
  4. 4
    Calculate probability: P(exactly one head)=24=12P(\text{exactly one head}) = \frac{2}{4} = \frac{1}{2}

Answer

P(exactly one head)=12P(\text{exactly one head}) = \frac{1}{2}
Enumerating the sample space systematically (using a tree or table) ensures no outcomes are missed. The probability of an event equals the number of favorable outcomes divided by the total number of equally likely outcomes.

About Sample Space

The sample space SS is the set of all possible outcomes of a random experiment — every outcome that could conceivably occur.

Learn more about Sample Space →

More Sample Space Examples

Example 1 easy

List the sample space for rolling a fair six-sided die, and verify that all probabilities sum to 1.

Example 3 easy

A bag contains one red, one blue, and one green marble. You draw one marble. Write the sample space

Example 4 medium

A spinner has 3 sections: Red (probability 0.5), Blue (probability 0.3), and Green. Find [formula] a

← All Sample Space Examples Sample Space Concept

Related Concepts

Probability