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Fairness and Bias

Maths: Edexcel GCSE Higher, topic 5.3.1

Fairness and Bias

When an event occurs, it can either be completely fair, or the outcome can be impacted by bias.

Definitions

Definitions

  • Fair event: Every result has an even probability of happening.
  • Biased: One or multiple results have a higher probability of happening than the rest, so they are not all the same.
Example 1

Example 1

  • A 6-sided dice is thrown, what should the chance of rolling a 2 be?
  • There is a 1x\dfrac{1}{x} chance of each outcome, and in this case there are 6 possible outcomes
  • Therefore the chance of a 2, or any number, being rolled is 16\dfrac{1}{6}
Example 2

Example 2

  • A spinner with 4 sections is spun; however, it is biased, so the chance of getting a 3 is twice as much as 1, 2, or 4. What is the probability of spinning a 3?
  • With the extra weighted chance of spinning a 3, the probabilities are calculated as x5\dfrac{x}{5}
  • The unbiased sides of 1,2 and 4 all have the probability of 15\dfrac{1}{5}, and the biased side of 3 will have the probability of 25\dfrac{2}{5}

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