An experiment is a repetition of a trial multiple times in order to observe how often each outcome occurs.

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

Experimental vs theoretical probability

Maths

Checking and securing displaying outcomes

Checking and securing exhaustive events

Probabilities involving algebra

Frequency trees

Checking and securing calculating probabilities from tables

Checking and securing calculating probabilities from diagrams

Experimental probability

Set notation

Conditional probability in a two-way table

Conditional probability in a Venn diagram

Conditional probability in a tree diagram

Algebra in tree and Venn diagrams

Constructing three event Venn diagrams

Probabilities in three event Venn diagrams

Comparing multiple representations to calculate conditional probabilities

Combinations

Advanced problem solving with conditional probability

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.

In this unit, pupils use their knowledge of calculating theoretical probabilities and extend it to calculate conditional probabilities.

Conditional probability

Predicting the outcome of flipping a fair coin

Predicting which way up a toy brick lands

Predicting the outcome of flipping a fair die

In which of these situations is it possible to work out a theoretical probability?

The coin is definitely biased towards heads.

The coin is definitely not biased towards heads.

The coin could be biased towards heads but more trials are needed to be sure.

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

Alex flips a coin 4 times. The coin lands heads 3 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 particular colour out of a bag of counters. In 1000 trials the number of times you should expect to draw a blue counter is {{}}.

A box contains 400 counters. A counter is drawn, its colour noted and replaced.  The results are in the table. Estimate how many red 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 prime number. P(prime) = {{ }} (as an unrounded decimal).

__________ probability can be determined by the number of times an event occurred during multiple trials.

A toy brick that is dropped could land in one of four possible ways. Jun drops the toy brick multiple times. Starting with the least likely outcome, place the outcomes in order of likelihood.

A toy brick that is dropped could land in one of four possible ways. Sofia and Jun drop the toy brick multiple times. Whose results should be the most reliable? Why?

A dropped cone could land in one of two ways. The bar chart shows the results from an experiment. Which calculation shows how to find the experimental probability of the cone landing curve down?

A dropped cone could land in one of two ways. The bar chart shows the results from an experiment. In an experiment with 800 trials you should expect the cone to land curve down {{ }} times.

Exit Quiz

In which of these situations is it possible to work out a theoretical probability?