Relative Frequency and Probability

statistics year12 standard

Relative frequency and probability | NSW Curriculum Website

• MST-12-S2-09 models and solves problems involving the probabilities of multistage events

📖 Prior Knowledge

Content	Prerequisite relationships
Chance A	- List equally likely outcomes → List the sample space - Represent probabilities as fractions → Calculate theoretical probability
Chance B	- Compare probabilities over many trials → Determine observed probability
Fractions Decimals Percentages	- Add and subtract fractions and mixed numbers → Find probabilities of complementary events - Solve problems with fractions and decimals of quantities → Calculate expected frequency
Probability	- List the sample space (revisited content) - Calculate theoretical probability (revisited content) - Determine observed probability (revisited content) - Identify the complement of an event → Find probabilities of complementary events - Find probabilities of complementary events (revisited content) - Calculate expected frequency (revisited content)
Probability A	- Distinguish independent and dependent events → Find probabilities of independent events - Record outcomes for multistage experiments (revisited content) - Calculate probabilities by counting multistage outcomes (revisited content) - Find probabilities of independent events (revisited content) - Find probabilities of dependent events (revisited content) - Use complements in multistage experiments (revisited content) - Apply the multiplication principle → Record outcomes for multistage experiments
Probability B	- Represent data in Venn diagrams and 2-way tables (revisited 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