← Maths Standard 2 syllabus

NSWMaths Standard 2

Year 11: Relative Frequency and Probability

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we predict how many times an event will happen over many trials?

Calculate the expected frequency of an event from the probability of the event and the number of trials, using expected frequency = P(E) x number of trials
A focused answer to the HSC Maths Standard 2 dot point on expected frequency. The rule expected frequency = P(E) times the number of trials, predicting how many times an event should happen over many trials, the expected-versus-observed difference, and working backwards to find the number of trials from an expected count, with worked Australian examples.
13 min answer →

How do we describe and measure the chance of an event in words and as a number between 0 and 1?

Describe the likelihood of an event using the language of chance and the probability scale from 0 to 1, distinguishing fair from biased and equally likely outcomes
A focused answer to the HSC Maths Standard 2 dot point on the language of probability. The likelihood scale from impossible to certain, describing chance in words and as a number between 0 and 1, even chance, likely and unlikely, the meaning of fair versus biased, and equally likely outcomes, with worked Australian examples.
13 min answer →

Why does every probability lie between 0 and 1, and how do complementary events help you find a chance the short way?

Recognise that probabilities of events range from 0 to 1, identify the complement of an event and use the relationship that the probability of an event and its complement sum to 1, so the probability of 'not E' equals 1 minus the probability of E
A focused answer to the HSC Maths Standard 2 dot point on the range of probabilities and complementary events. Why every probability sits between 0 and 1, what the complement of an event is, the rule that an event and its complement add to 1 so the probability of not E is 1 minus the probability of E, and the at-least-one short cut, with worked Australian examples.
13 min answer →

How do we estimate a probability from experimental data using relative frequency, and why does the estimate settle toward the theoretical probability as more trials are run?

Calculate relative frequencies to estimate probabilities of events, where relative frequency = frequency of the event divided by the total number of trials, recognising that as the number of trials increases the relative frequency approaches the theoretical probability
A focused answer to the HSC Maths Standard 2 dot point on relative frequency. Relative frequency as frequency divided by total, using it as an experimental probability, estimating the chance of a real event from collected data, and the long-run convergence of relative frequency toward the theoretical probability, with worked Australian examples.
13 min answer →

How do tree diagrams and two-way tables find probabilities for multi-stage events?

Use arrays and tree diagrams to determine the outcomes and probabilities for multi-stage experiments, including two-way tables, multiplying probabilities along the branches of a tree diagram and adding the probabilities of mutually exclusive outcomes, with and without replacement
A focused answer to the HSC Maths Standard 2 dot point on multi-stage events. Two-way tables, tree diagrams for two- and three-stage experiments, the difference between drawing with and without replacement, multiplying probabilities along the branches and adding across mutually exclusive paths, with worked coin, counter and survey examples.
15 min answer →

How do we calculate the theoretical probability of an event from its sample space?

List the sample space of equally likely outcomes and calculate the theoretical probability of an event using $P(E)=\dfrac{n(E)}{n(S)}$ , the number of favourable outcomes divided by the total number of outcomes
A focused answer to the HSC Maths Standard 2 dot point on theoretical probability. Listing a sample space systematically, equally likely outcomes, the formula P(E) = n(E)/n(S), and finding the probability of single and described compound events on dice and cards, with worked Australian examples.
14 min answer →