Variation 2 · answer guide

Binomial distribution — At most phrasing

Question

In independent trials, is the sample proportion of successes. equals

This practice question was inspired by Question 2 in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: identify the random variable and its parameters before using the matching probability formula.At most successes .
Finish the calculation, then check that the result meets the question’s conditions.Option C confuses count with proportion.
Match the result to the choices and state the correct option.Therefore option A is correct.

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

Verification: Proportion = count / .

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