2025 HSC Mathematics Extension 1
Question 13(d):
Binomial distribution
A counter is selected from a bag, its colour recorded, and then replaced; this is repeated times. Let count the green selections. Given and , use the standard normal approximation to find .
How to recognise this question
Question type: binomial distribution
- The command and notation point to binomial distribution.
- The requested response is a worked solution.
How to handle it: identify the random variable and its parameters before using the matching probability formula.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- , so .
- , so .
- means , corresponding to .
- , so .
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 4 total marks for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
If , find .
Question 2
A trial succeeds with probability . For five independent trials, find the probability of at least one success.
Question 3
For , find the mean and variance.