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MathidiaMathematics Academy
Statistical distributions
Lesson 55 of 75
Review

Binomial modelling

Objective. Assess whether a binomial model is appropriate.

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

Learn: the key idea

Binomial modelling means judging whether real data or a described scenario genuinely satisfies the binomial assumptions before trusting calculated probabilities. You must assess independence (does one trial affect another?), constant probability (does p change over time or with sampling?), and a fixed number of trials. For example, modelling defective items from a large batch as binomial is reasonable since removing a few items barely changes the proportion defective, but modelling repeated matches of the same two tennis players may fail if form changes. Good modelling states assumptions explicitly and considers how reasonable they are in context.

Worked example

Give one reason why modelling the number of rainy days in a week as binomial might be inappropriate for binomial modelling.

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Illustrated card showing ?
  1. 1Binomial requires trials to be independent
  2. 2Weather on consecutive days is often correlated, not independent
  3. 3A rainy day today increases the chance of rain tomorrow
  4. 4Therefore independence fails, making the binomial model inappropriate

Answer: Rainy days are not independent from day to day

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Common mistake. Students assume any repeated trial is automatically binomial without checking independence, such as assuming successive exam attempts have constant pass probability. Always state and justify each binomial condition against the real context.

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