1. 9. Relative frequency and probability
Study guide
9. Relative frequency and probability

2. Relative frequency
Relative frequency estimates the chance of something happening or the probability of an event. It is the frequency of the event divided by the total number of frequencies.
HSC Hint – Relative frequency is expressed using fractions, decimals and percentages.

3. Multistage events
Multistage events consists of two or more events. For example, tossing a coin and throwing a die.
HSC Hint – The result of the first event may not affect the result of the second event (independent events).

4. Fundamental counting principle
The fundamental counting principle is used to determine the total number of outcomes for a multistage event. It states if we have ‘p’ outcomes for first event and ‘q’ outcomes for the second event, then the total number of outcomes for both events is p × q.
Number of outcomes (two events) = p × q.
p – Number of outcomes of the first event.
q – Number of outcomes of the second event.
HSC Hint – Multiply the number of outcomes for each event to determine the number of items in the sample space.

5. Systematic lists – Table
Outcomes for the first event are listed down the first column. Outcomes for the second event are listed across the top row.
Head
Tail HH HT TH TT
HSC Hint – Each cell in a table is an outcome.

6. Systematic lists – Tree diagram
Outcomes for each event are listed down the page with the events extending across the page. Each event is a new branch of the tree. The sample space is listed on the right-hand side.
HSC Hint – Always draw large tree diagrams and list the sample space on the right-hand side.

7. Definition of probability
Probability is the chance of something happening. The probability of the event is calculated by dividing the number of favourable outcomes by the total number of outcomes.
HSC Hint – Probabilities expressed as a fraction need to be simplified if possible.

8. Range of probability Probability of an event that is impossible is 0.
Probability of an event that is certain is 1.
Probability of an event is between 0 and 1 or
A, B,.. are all the possible outcomes or events.
HSC Hint – Probability of an event is never larger that one or a negative number.

9. Complementary events
Complementary events are the outcomes that are not members of the event. Probability of an event and its complement will sum to be 1.
E ‒ Event or outcome.
‒ Complement of event E or the outcomes not including event E.
HSC Hint – Read the question carefully and decide whether the probability of the complement is required.