Variation 1 · answer guide

Binomial distribution — Different success count

Question

A coin is tossed times. Let be the proportion of heads. The probability of at least heads 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 at least heads means .
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: Equality is included by "at least".

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