Variation 3 · answer guide
Binomial distribution — Probabilities given by a rule
Question
A random variable takes the values and , with . What are the mean and variance of ?
This practice question was inspired by Question 4 in the 2025 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
- Set up the solution: identify the random variable and its parameters before using the matching probability formula. and , so .
- Simplify the previous line carefully, keeping exact values where possible..
- Finish the calculation, then check that the result meets the question’s conditions..
- Match the result to the choices and state the correct option.Therefore option C is correct.
Common mistake: changing so many features that the new example no longer tests the same mathematical idea.
Verification: The probabilities add to , and .
Any mark labels are a TestMum study aid, not an official NESA marking allocation.
← Back to 2025 HSC Extension 1 paper Question 4