A theoretical probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely.

Calculating theoretical probabilities from two-way tables (two events)

Maths

Checking listing possible outcomes

The probability scale

Calculating theoretical probabilities from lists (one event)

Calculating theoretical probabilities from a table (one event)

Calculating theoretical probabilities from probability tree diagrams (one event)

Calculating theoretical probabilities from Venn diagrams (one event)

Comparing multiple representations to calculate theoretical probabilities

Summing probabilities

Calculating theoretical probabilities from Venn diagrams (two events)

Calculating theoretical probabilities from probability trees (two events)

Comparing multiple representations to calculate theoretical probabilities for combined events

Problem solving with theoretical probability

In the future unit, pupils use their knowledge of calculating theoretical probabilities and extend this understanding to calculating conditional probabilities using all of the representations encountered in this unit.

In the prior unit, pupils learnt techniques for systematically listing all of the possible outcomes for both one event and two events. In this unit, pupils use lists of outcomes to find theoretical probabilities. 

In this unit we build upon the concept of likelihood to work more mathematically with more measurable probability using fraction and decimal representations to both interpret and calculate. We revisit and develop ways to represent and compare probabilities.

Probability: theoretical probabilities

If this spinner is spun twice, what is the probability that the sum of both results would be 11?

If this spinner is spun twice, what is the probability of not losing either time?

If this spinner is spun twice, what is the probability that the sum of both results would be odd?

If spun twice what is the probability this spinner would spell 'pea' then 'nut' ?

If each of these spinners is spun once, what is the probability of getting H and 6?

If this spinner is spun twice, what is the probability of the sum of the results being less than 10?

In a fair six-sided die, what is the probability of rolling a 5 and getting a head in a single toss of a fair coin?

ξ = {AA, AB, AC, BA, BB, BC, CA, CB, CC}

A counter is taken from the bag. Its letter is noted and then it is placed back into the bag. A counter is taken from the bag again. Which of these options is not the correct sample space?

If the probability of an event (A) is $$/frac{3}{7}$$, and the experiment is repeated 49 times, what is the theoretical number of times event (A) will occur?

Which of the events {A,B,C} is the least likely to occur according to this probability tree?

John uses an unbiased random selection tool to generate a single letter of the alphabet. It is repeated three times. Which of the following letter sequences is the least likely?

The total number of possible outcomes in Trial 1 is greater than in Trial 2.

The total number of possible outcomes in Trial 1 is less than in Trial 2.

The total number of possible outcomes in Trial 1 is the same are in Trial 2.

There are two trials. In Trial 1, a spinner with {A, B} is spun twice. In Trial 2, a spinner with {B, C} is spun twice. Which statement is true?

Calculating theoretical probabilities from two-way tables (two events)

Lesson outcome