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MathidiaMathematics Academy
Probability models
Lesson 70 of 75
Review

Probability puzzles

Objective. Solve multi-step chance problems and critique assumptions.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Probability puzzles often require combining several rules, such as mutually exclusive addition or independent event multiplication, across multiple steps rather than a single calculation. Careful reading identifies whether events are independent, mutually exclusive, or conditional on each other, since this determines which rule applies at each stage. It also helps to question whether stated assumptions, like equally likely outcomes, are realistic for the context given. Example: finding the probability of drawing two reds without replacement from a bag requires multiplying changing probabilities at each stage, since the second draw depends on the first.

Worked example

A bag contains 5 red and 3 blue counters. Two counters are drawn without replacement. Find the probability that both counters are red, as part of this probability puzzle.

5 … 3
Illustrated card showing 5 … 3
  1. 1Find the probability the first counter is red: 5 out of 8 total counters.
  2. 2After removing one red, 4 red counters remain out of 7 total counters.
  3. 3Multiply the two probabilities: (5/8) × (4/7).
  4. 4This gives 20/56, which simplifies to 5/14.

Answer: 5/14

Concept mastery

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Practice

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Common mistake. Pupils often use the same probability for both draws in without-replacement problems, forgetting the total number of items decreases after the first draw; always adjust the denominator for the second event.

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