AI generatedProbabilityKey Stage 3

Assessing fairness from results

Assessing fairness from results.

  • 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 spinner with two equal sectors is spun 100 times: red 75, blue 25. Comment on whether the results support fairness.

Expected redA fair spinner gives each equal sector probability .
Observed redCompare the result with the expected count.
Red occurs much more often than expected. This gives reason to investigate the spinner or method, but these results alone do not prove unfairness.

Example 2

A spinner with two equal sectors is spun 110 times: red 81, blue 29. Comment on whether the results support fairness.

Expected redA fair spinner gives each equal sector probability .
Observed redCompare the result with the expected count.
Red occurs much more often than expected. This gives reason to investigate the spinner or method, but these results alone do not prove unfairness.

Your turn

Question 1

A spinner with two equal sectors is spun 120 times: red 87, blue 33. Comment on whether the results support fairness.

Check answer
Expected redA fair spinner gives each equal sector probability .
Observed redCompare the result with the expected count.
Red occurs much more often than expected. This gives reason to investigate the spinner or method, but these results alone do not prove unfairness.
Question 2

A spinner with two equal sectors is spun 130 times: red 93, blue 37. Comment on whether the results support fairness.

Check answer
Expected redA fair spinner gives each equal sector probability .
Observed redCompare the result with the expected count.
Red occurs much more often than expected. This gives reason to investigate the spinner or method, but these results alone do not prove unfairness.
Question 3

A spinner with two equal sectors is spun 140 times: red 99, blue 41. Comment on whether the results support fairness.

Check answer
Expected redA fair spinner gives each equal sector probability .
Observed redCompare the result with the expected count.
Red occurs much more often than expected. This gives reason to investigate the spinner or method, but these results alone do not prove unfairness.
Question 4

A spinner with two equal sectors is spun 150 times: red 105, blue 45. Comment on whether the results support fairness.

Check answer
Expected redA fair spinner gives each equal sector probability .
Observed redCompare the result with the expected count.
Red occurs much more often than expected. This gives reason to investigate the spinner or method, but these results alone do not prove unfairness.
Question 5

A spinner with two equal sectors is spun 160 times: red 111, blue 49. Comment on whether the results support fairness.

Check answer
Expected redA fair spinner gives each equal sector probability .
Observed redCompare the result with the expected count.
Red occurs much more often than expected. This gives reason to investigate the spinner or method, but these results alone do not prove unfairness.