Variation 3 · answer guide

Binomial distribution — Irreducible fraction threshold

Question

A die is rolled times; is the proportion of sixes. Probability of at least sixes is

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., so .
Finish the calculation, then check that the result meets the question’s conditions. is the theoretical success probability, not the threshold for this event.
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: Always convert count to proportion by dividing by .

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