Compound Events Examples in Statistics

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

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

Concept Recap

Compound events are probability events made up of two or more simple events combined using 'and' (both events occur) or 'or' (at least one occurs). For independent 'and' events, multiply probabilities; for 'or' events, add probabilities and subtract any overlap.

Simple event: rolling a 6. Compound event: rolling a 6 AND then flipping heads. For 'and,' multiply probabilities. For 'or,' add them (but subtract overlap if any).

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: For independent 'and' events, multiply probabilities. For mutually exclusive 'or' events, add probabilities. For overlapping 'or' events, subtract the overlap.

Common stuck point: Students add probabilities for 'and' events instead of multiplying, or forget to subtract the overlap when computing 'or' for non-mutually-exclusive events.

Sense of Study hint: First, identify whether the compound event uses 'and' or 'or.' For 'and,' multiply the individual probabilities. For 'or,' add the probabilities, but if the events can overlap, subtract the probability of both happening: P(A or B) = P(A) + P(B) - P(A and B).

Worked Examples

Example 1

easy
A bag contains 3 red and 5 blue marbles. You draw one marble, replace it, then draw another. What is the probability of getting red then blue?

Solution

  1. 1
    Step 1: Since the marble is replaced, the draws are independent events.
  2. 2
    Step 2: P(\text{red}) = \frac{3}{8}, P(\text{blue}) = \frac{5}{8}.
  3. 3
    Step 3: For independent events: P(\text{red then blue}) = P(\text{red}) \times P(\text{blue}) = \frac{3}{8} \times \frac{5}{8} = \frac{15}{64}.

Answer

P(\text{red then blue}) = \frac{15}{64} \approx 0.234.
Compound events involve two or more simple events. When events are independent (one does not affect the other), the probability of both occurring is the product of their individual probabilities. Replacement ensures independence between draws.

Example 2

medium
A bag contains 4 red and 6 blue marbles. You draw two marbles without replacement. What is the probability that both are red?

Practice Problems

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

Example 1

medium
A spinner has sections: Red (50%), Blue (30%), Green (20%). You spin twice. What is the probability of getting the same colour both times?

Example 2

hard
A deck has 52 cards. You draw 2 cards without replacement. What is the probability of drawing at least one ace?
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Background Knowledge

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

probability basicstat sample space