When listing outcomes systematically, they are listed in such a way as to ensure all outcomes are recorded.

Checking listing possible outcomes

Maths

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 two-way tables (two events)

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

When listing outcomes {{}}, they are listed in such a way as to ensure all outcomes are recorded. 

A coin is flipped twice. Complete the sample space ξ = {HH, HT, TH, {{}}}

A coin is flipped three times. Which outcome is missing from the following sample space? ξ = {HHH, HHT, HTH, HTT, THH, THT, {{}}, TTT}

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

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 is a correct sample space for this trial?

In a rugby match, a team can either win (W), lose (L) or draw (D). A team plays two matches. Which outcome is missing from the following sample space? ξ = {WW, WL, WD, LW, LL, DW, DL, DD}

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, C} is spun twice. In Trial 2, a spinner with {A, B} is spun three times. Which statement is true?

a representation used to model probability questions

A {{}} is all the possible outcomes of a trial.

Which of these numbers is not on a standard six-sided dice?

A spinner containing "win" and "lose" is spun.

A bag contains tiles each of which is a vowel. A tile is picked.

Complete the following sample space for the outcomes of the spinner. ξ = {A, I, L, T, {{ }} }.

How many possible outcomes are there on this spinner?

Starter Quiz

In probability, what is a 'trial'?