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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Presentation

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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.