Free Year 12 Probability & statistics Quiz — 10 Questions, Instant Results

Free practice quizzes › Year 12 Maths (VCE) quiz › Probability & statistics

What Year 12 students need to know about probability and statistics

A short orientation first. Year 12 probability and statistics covers discrete random variables, the binomial distribution, continuous random variables, the normal distribution, sample proportions and confidence intervals, and the use of a CAS to compute probabilities.

Our tutors wrote and checked these questions against the VCE study design, which is why the wording and the difficulty match what a Year 12 student meets at school.

The usual probability and statistics errors at Year 12

If your child gets a question wrong here, it is worth checking whether one of these is behind it. They are the probability and statistics misconceptions RHZ tutors correct most often with Year 12 students:

• Conditional probability is calculated with the wrong denominator.
• A box plot is read as showing frequencies.
• Correlation is treated as proof of causation.

Spotting which one applies is the useful part; the fix is usually quick once the misunderstanding is out in the open.

How to practise probability and statistics at home

Practice works when it is short, regular and specific. For probability and statistics, our tutors suggest:

1. Use technology to find standard deviation, then explain what it means.
2. Practise conditional probability from two-way tables.
3. Draw box plots from raw data by hand.

For VCE maths, fluency in the foundations frees up working memory for the extended questions. Do a short mixed set daily and a timed paper each fortnight.

How this probability and statistics quiz works

We keep 18 probability and statistics questions for Year 12 that meet our standard, at the easy and at-level tiers, and this page serves 10 of them at a time. The default set is stable, so a teacher or parent can share the link; a fresh set is one click away. Marking happens on our server so the answer key cannot be read from the page.

Because every question here is on probability and statistics, a low score is a clear signal and a high score is genuinely reassuring for this topic. What it cannot tell you is whether the other Year 12 maths topics are equally secure, or how far above the year level the student can go; the free Skills Check covers both.

The quiz: 10 questions

Choose one answer for each question, then press Mark my answers. Set 87640 · New set of questions →

Question 1

Probability & statistics

A continuous random variable X has probability density function f(x) = k/x² for 1 ≤ x ≤ 4, and f(x) = 0 otherwise. What is the value of k?

k = 4/15 k = 4/3 k = 1/3 k = 3/4

Question 2

Probability & statistics

A factory produces bolts with diameters normally distributed with mean 10 mm and standard deviation 0.2 mm. A bolt is rejected if its diameter is more than 0.35 mm from the mean. Using the standard normal table where P(Z < 1.75) = 0.9599, what percentage of bolts are rejected?

4.01% 5.00% 8.02% 91.98%

Question 3

Probability & statistics

A continuous random variable X has probability density function f(x) = kx² for 0 ≤ x ≤ 3, and f(x) = 0 otherwise. What is the value of k, and what is E(X)?

k = 1/9, E(X) = 3 k = 1/3, E(X) = 3/4 k = 1/9, E(X) = 9/4 k = 1/27, E(X) = 9/4

Question 4

Probability & statistics

A bag contains 4 red and 6 blue marbles. Two marbles are drawn without replacement. Given that the first marble drawn is red, what is the probability that both marbles are red?

3/9 4/10 × 3/9 3/10 4/10

Question 5

Probability & statistics

A die is rolled once. The expected score is?

3.5 6 3 4

Question 6

Probability & statistics

A discrete random variable X takes values 1, 2, 3 only. It is known that E(X) = 2 and E(X²) = 5. Let Y = 2X − 1. Which of the following gives the correct value of Var(Y)?

4 16 1 2

Question 7

Probability & statistics

A random variable X has E(X) = 5 and Var(X) = 4. Let Y = 3X − 2. What is the standard deviation of Y?

10 6 12 36

Question 8

Probability & statistics

A larger standard deviation means the data is?

smaller more clustered all equal more spread out

Question 9

Probability & statistics

Median of 2, 9, 4, 7, 6 is?

7 28 6 4

Question 10

Probability & statistics

P(A)=0.4, P(B)=0.5, independent. P(A and B)?

0.45 0.2 0.1 0.9

Mark my answers →

Your result

0 / 10

Take the free full Skills Check →   Try another set

How to read a score out of 10

9 or 10 out of 10

The easy and at-level content is secure. The useful question now is how far above the year level the student can go, which a ten-item quiz cannot show. The free Skills Check adds stretch and challenge questions on every topic so you can see the ceiling as well as the floor.

7 or 8 out of 10

Solid, with one or two specific gaps. Look at which topic the incorrect answers came from (the results panel names the weakest topic) and spend a week on that topic before re-testing with a different seed.

5 or 6 out of 10

Some core ideas are shaky. The pattern matters more than the score: two misses in the same topic is a gap; misses scattered across topics usually means reading the question too fast. Either way, the Skills Check will tell you which.

4 or fewer out of 10

Foundations from an earlier year are probably missing, which is common and fixable. Try the quiz one year level down to confirm, then talk to a tutor about a short catch-up plan rather than more of the same practice.

What to do with the result

Questions? Call 03 9509 3293 or book a free consultation. RHZ Tutoring, 17/47 Apex Drive, Truganina VIC 3029.

Frequently asked questions

Other Maths topics for Year 12

Mixed Year 12 Maths (VCE) quiz (all topics) →

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