AI generatedProbabilityKey Stage 3

Comparing experimental and theoretical probability

Comparing experimental and theoretical probability.

  • Probability = favourable outcomes ÷ all outcomes when individual outcomes are equally likely.
  • A probability lies between 0 and 1; complementary probabilities sum to 1.
  • Experimental relative frequency estimates probability and can vary between samples.

Example 1

A fair six-section spinner has 1 winning sections. It wins 12 times in 60 spins. Compare the experimental and theoretical probabilities.

Use the equally likely sections.Use the observed results.
The experimental probability is higher in this sample. Random variation can cause a difference.

Example 2

A fair six-section spinner has 2 winning sections. It wins 19 times in 66 spins. Compare the experimental and theoretical probabilities.

Use the equally likely sections.Use the observed results.
The experimental probability is lower in this sample. Random variation can cause a difference.

Your turn

Question 1

A fair six-section spinner has 3 winning sections. It wins 40 times in 72 spins. Compare the experimental and theoretical probabilities.

Check answer
Use the equally likely sections.Use the observed results.
The experimental probability is higher in this sample. Random variation can cause a difference.
Question 2

A fair six-section spinner has 4 winning sections. It wins 47 times in 78 spins. Compare the experimental and theoretical probabilities.

Check answer
Use the equally likely sections.Use the observed results.
The experimental probability is lower in this sample. Random variation can cause a difference.
Question 3

A fair six-section spinner has 1 winning sections. It wins 16 times in 84 spins. Compare the experimental and theoretical probabilities.

Check answer
Use the equally likely sections.Use the observed results.
The experimental probability is higher in this sample. Random variation can cause a difference.
Question 4

A fair six-section spinner has 2 winning sections. It wins 27 times in 90 spins. Compare the experimental and theoretical probabilities.

Check answer
Use the equally likely sections.Use the observed results.
The experimental probability is lower in this sample. Random variation can cause a difference.
Question 5

A fair six-section spinner has 3 winning sections. It wins 52 times in 96 spins. Compare the experimental and theoretical probabilities.

Check answer
Use the equally likely sections.Use the observed results.
The experimental probability is higher in this sample. Random variation can cause a difference.
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