2021 HSC Mathematics Extension 1
Question 6:
Binomial distribution
The random variable represents the number of successes in independent Bernoulli trials. The probability of success is in each trial.
Let . Which of the following describes the value of ?
How to recognise this question
Question type: binomial distribution
- The command and notation point to binomial distribution.
- The requested response is a multiple choice.
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 .
- Since is tiny and positive, is extremely close to , and in particular .
- More generally, for and , when and is not too extreme — here the comparison with is immediate because .
- Answer: A. (NESA multiple-choice key: A.)
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark 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 and , which is true?
Question 2
If and , which is true?
Question 3
If and , which best describes ?