#Statistics #Year12 #Standard >[!info]- [Relative frequency and probability | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-standard-11-12-2024/content/n12-tba2/fae778ced4) >- MST-12-S2-09 models and solves problems involving the probabilities of multistage events ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | ------------------------------------ | ------------------------------------------- | -------------------- | | [[Stage 4/Probability\|Probability]] | - basic probability<br>- relative frequency | - *repeated content* | | [[Probability A]] | - multistage probability | - *repeated content* | | [[Probability B]] | - Venn diagrams and two-way tables | - *repeated content* | ## Relative frequency and probability - Recognise that probabilities range from 0 (impossible) to 1 (certain) and can be represented as fractions, decimals and percentages - Identify and define the sample space as the set of all possible outcomes of a chance experiment - Determine the number of outcomes for an experiment - Express the probability of an event that has a finite number of equally likely outcomes, as $P(\text{event})=\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$ - Apply $P(\text{an event does not occur})=1-P(\text{the event does occur})$ to calculate the probability of the complement of an event - Construct and use arrays, tree diagrams and probability trees to determine the outcomes and probabilities for multistage events - Determine the probabilities of outcomes for multistage events using $P(A \text{ and } B)=P(A)\times P(B)$ - Use relative frequency as an estimate of probability - Recognise that increasing the number of trials produces relative frequencies that become closer in value to the theoretical probability - Calculate the expected frequency of an event occurring using np where n is the number of times an experiment is repeated, and p is the probability that the event occurs on each of those times - Construct and interpret Venn diagrams and two-way tables from given information, limited to combinations of two attributes, and use them to solve problems in a variety of contexts - Examine the use of statistics and the associated probabilities in shaping decisions made by the media, governments and companies