Calculating theoretical probabilities from lists (one event) | Maths

Starter quiz

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

'probability' ✓
Which letter on the probability scale represents a probability of 0.5?

A

B

C ✓

D

E
$The spinner is divided into equal-sized sectors. What fraction of the spinner is labelled 'win'?$

The spinner is divided into equal-sized sectors. What fraction of the spinner is labelled 'win'?

${1}\over{2}$

${1}\over{3}$

${2}\over{3}$

${2}\over{5}$ ✓
The spinner is divided into equal-sized sectors. ______% of the spinner is labelled 'lose'.

'60' ✓
A trial has three possible outcomes: {A, B, C}. P(A) = ${2}\over{7}$ . P(B) = ${1}\over{7}$ . P(C) = ${4}\over{7}$ . Which outcome is most likely to happen?

A

B

C ✓
The probability on an outcome is 25%. Approximately how many times could you expect the outcome to occur in 500 trials?

25

50

100

125 ✓

250

Exit quiz

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

An experimental

An exact

A likelihood

A theoretical ✓
What is the probability that this spinner lands on 'A'?

${1}\over{2}$

${1}\over{3}$

${1}\over{4}$ ✓

${1}\over{5}$
What is the probability that this spinner lands on 'win'?

${1}\over{2}$

${1}\over{3}$

${3}\over{4}$

${3}\over{7}$ ✓
A counter is picked at random from the bag. What is the probability that it contains the letter B?

${1}\over{2}$

${1}\over{3}$

${3}\over{5}$

${3}\over{8}$ ✓
A regular six-sided dice is rolled. What is the probability of rolling a 4?

${1}\over{2}$

${1}\over{4}$

${1}\over{5}$

${1}\over{6}$ ✓

${4}\over{6}$
A regular six-sided dice is rolled. Which event has a probability of ${4}\over{6}$ ?

rolling a cube number

rolling an even number

rolling a factor of 6 ✓

rolling a prime number

rolling a square number

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Lesson Details

Key learning points

The probability of an outcome can be found by considering the list of all possible outcomes.
The probability of a set of outcomes can be found by considering the list of all possible outcomes.
A list of all possible outcomes can help us find a probability, even when the outcomes are not equally likely.

Common misconception

Pupils may assume that theoretical probabilities can be also found in cases where individual outcomes are not equally likely (e.g. picking a sweet out of a box where the sweets are different shapes).

If the sweets in a box are different shapes then picking a sweet out of the box is not necessarily random. Someone could find their favourite flavour sweet by feeling the different shapes.

Keywords

Theoretical probabilities - 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.