Variation 1 · answer guide

Binomial distribution — At least 3 of 4 guesses

Question

An applicant has correct already and needs of . They randomly guess remaining four-option items. Probability of at least correct is

This practice question was inspired by Question 7 in the 2024 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.Need with .
Finish the calculation, then check that the result meets the question’s conditions. is exactly option A.
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: Numeric value: .

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