The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.

Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.

Tree diagrams are a representation used to model statistical/probability questions. Branches represent different possible events or outcomes.

Set notation

Maths

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

Conditional probability

Which symbol is used to represent the universal set?

What region is shown shaded in this Venn diagram? 

ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, A = {multiples of 4}, B = {factors of 12}. Find P(A' ∩ B).

Which combination of events is highlighted in the tree diagram?

Lucas and Izzy each play one game of chess that they can either win or lose. P(Lucas wins ∪ Izzy wins) = {{ }} (give your answer as a decimal). 

Predicting the winner in a game of tennis

Predicting which way up a toy brick lands

Predicting the outcome of flipping a fair coin

Predicting the outcome of spinning a fair spinner

In which of these situations is it not possible to work out a theoretical probability?

The die could be fair but more trials are needed to be sure.

The die is definitely biased towards a 6.

The die is definitely not biased towards a 6.

The die could be biased but more trials are needed to be sure.

Izzy rolls a die 4 times. The dice lands on a '6' three times. Which of these statements are correct?

A spinner contains three letters: A, B and C. The tables show results from four experiments with the spinner. Which experiment will produce the most reliable set of experimental probabilities?

The table shows the theoretical probabilities of taking a counter of a specific colour out of a bag of counters. In 1000 trials, the number of times you should expect to draw a green counter is {{}}.

A box contains 100 counters. A counter is drawn, its colour noted and replaced. The results are in the table. Estimate how many green counters are in the box.

A class investigates whether a 6-sided die is biased. The table shows the results. Estimate the probability of the die landing on a factor of 6. P(factor of 6) = {{ }} (as an unrounded decimal).

Starter Quiz