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← 2022 HSC Extension 1 paper Question 12(e)

Variation 1 · answer guide

Binomial distribution — New rewards

Question

Same bag, 4 draws with replacement; red , green . Expected score?

This practice question was inspired by Question 12(e) in the 2022 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Step by step

  1. Set up the solution: identify the random variable and its parameters before using the matching probability formula.One draw: .
  2. State the final answer clearly in the form the question requested.Four draws: .

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Linearity of expectation.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.

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