Basic Probability Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Basic Probability.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

Probability is the measure of how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain). It is calculated as the ratio of favorable outcomes to total possible outcomes when all outcomes are equally likely.

Probability is a way of putting a number on chance. Flipping heads? That's 0.5 (half the time). Rolling a 6 on a die? That's \frac{1}{6} (one out of six possible outcomes). It's like asking 'if we did this many times, what fraction would this outcome happen?'

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Probability assigns a number between 0 and 1 to the likelihood of an event. The sum of probabilities of all possible outcomes always equals 1.

Common stuck point: Students confuse short-run results with long-run probability — getting 3 heads in 4 flips does not mean heads is 'more likely' than 0.5.

Sense of Study hint: First, list all possible outcomes (the sample space). Then count how many of those outcomes are favorable (the event you care about). Finally, divide: P(event) = favorable outcomes / total outcomes. The result should be between 0 and 1.

Worked Examples

Example 1

easy
A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of drawing a blue marble?

Solution

  1. 1
    Step 1: Total marbles = 3 + 5 + 2 = 10.
  2. 2
    Step 2: Favourable outcomes (blue) = 5.
  3. 3
    Step 3: P(\text{blue}) = \frac{5}{10} = \frac{1}{2}.

Answer

\frac{1}{2}
Basic probability is the ratio of favourable outcomes to total possible outcomes, assuming each outcome is equally likely.

Example 2

easy
A fair six-sided die is rolled. What is the probability of rolling an even number?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A spinner has 8 equal sections numbered 1–8. What is the probability of landing on a number greater than 5?

Example 2

easy
A card numbered 1 through 10 is chosen at random. What is the probability that the number is prime?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

relative frequency