An outcome is a result of a trial (e.g. getting heads when flipping a coin once or getting two heads when flipping a coin twice).

An event is a subset of a sample space. i.e. An outcome or set of outcomes that may occur from a trial (e.g. flipping a coin twice and getting the same result each time).

Each branch of a probability tree shows a possible outcome from an event or from a stage of a trial, along with the probability of that outcome happening.

A sample space is all the possible outcomes of a trial. A sample space diagram is a systematic way of producing a sample space.

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

Calculating theoretical probabilities from Venn diagrams (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 P(A) = $$\frac{1}{3}$$ and P(A and D) = $$\frac{1}{5}$$, then what is P(D)? 

Events B and F should sum to 1 but they don't.

Events A and C should sum to 1 but they don't.

Events D and E should sum to 1 but they don't.

Events E and F should sum to 1 but they don't.

What is a suitable calculation for the probability of event B occurring, and event F not occurring?

If the first and second event in this tree diagram were both flipping a coin once, what would be the probability of event B and event F occurring?

What is the least likely (but not impossible) pair of events occurring in this tree diagram?

Which pair of events has a more than even chance of occurring?

What is the sum of the possible events A, B and C in this probability tree?

In a fair six-sided die, what is the probability of rolling a 2 and getting 'tails' in a single toss of a fair coin?

A and C have an equal chance of appearing in the trials.

B is more likely to appear in the trials.

B is less likely to appear in the trials than A. 

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 statements are true?

What is the probability of this spinner landing on a vowel?

Alex is incorrect, it is less likely the spinner would land on a shaded space.

Alex is incorrect, it is more likely the spinner would land on a shaded space.

Alex believes that the likelihood of a spinner stopping on a shaded space is equal to an unshaded space. Is Alex correct?

How many ways are there to get a sum of 7 when adding the results of two standard six-sided dice rolls? 

This lesson was made for home learning during the pandemic.

Calculating theoretical probabilities from probability trees (two events)

Lesson outcome

This lesson was made for home learning during the pandemic.