Summing probabilities | Maths | Quizalize & Oak National Academy

Starter quiz

A __________ diagram is a representation used to model statistical/probability questions, where branches represent different possible events or outcomes.

'tree' ✓
What is the probability that the spinner lands on the number 2?

${1}\over{2}$

${1}\over{3}$ ✓

${2}\over{3}$

${2}\over{6}$
What is the probability that the spinner does not land on the number 2?

${1}\over{2}$

${1}\over{3}$

${2}\over{3}$ ✓

${2}\over{6}$
Which values represent the probability that this spinner lands on an integer?

${1}\over{3}$

1 ✓

1%

100% ✓

${3}\over{3}$ ✓
Based on the Venn diagram, which numbers belong to both sets A and B?

1

2

3 ✓

6 ✓

9
An integer between 1 and 10 is selected at random. Based on the Venn diagram, what is the probability that the outcome is from set A?

${1}\over{7}$

${3}\over{7}$

${1}\over{10}$

${3}\over{10}$ ✓

${9}\over{10}$

Exit quiz

Two or more events are __________ if they share no common outcome.

certain

exhaustive

impossible

likely

mutually exclusive ✓
A set of events are __________ if at least one of them has to occur whenever the experiment is carried out.

certain

exhaustive ✓

impossible

likely

mutually exclusive
A standard six-sided dice is rolled. Which pairs of events are mutually exclusive?

{odd, even} ✓

{prime, even}

{factor of 6, multiple of 6}

{6, lower than 6} ✓

{prime, square} ✓
A standard six-sided dice is rolled. Which pairs of events are exhaustive?

{odd, even} ✓

{prime, even}

{factor of 6, multiple of 6} ✓

{6, lower than 6} ✓

{prime, square}
When a set of events are all mutually exclusive and exhaustive, their probabilities sum to ______.

'1' ✓
The probability that a cone lands on its base is 0.1. What is the probability that the cone does not land on its base?

'0.9' ✓

Worksheet

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Lesson Details

Key learning points

Summing the probabilities of all possible unique outcomes for a trial gives 1
Summing the probabilities of non-unique events gives a value not equal to 1
Knowing that the probabilities of all possible unique outcomes sum to 1 can be used to find unknown probabilities.
Knowing that probabilities can sum to 1 can be used to find unknown probabilities (different denominators).

Common misconception

Pupils may over generalise and think that the sum of all possible events sum to 1. E.g. when rolling a standard six-sided dice, P(multiple of 6) + P(factor of 6) = 1.

Emphasise that probabilities sum to 1 when the events are mutually exclusive and exhaustive. E.g. in the calculation P(multiple of 6) + P(factor of 6), the outcome '6' is counted twice.

Keywords

Mutually exclusive - Two events are mutually exclusive if they share no common outcome.