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Year 9

Summing probabilities

I can show that the probabilities of all possible unique outcomes for a trial, sum to one.

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New
New
Year 9

Summing probabilities

I can show that the probabilities of all possible unique outcomes for a trial, sum to one.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Summing the probabilities of all possible unique outcomes for a trial gives 1
  2. Summing the probabilities of non-unique events gives a value not equal to 1
  3. Knowing that the probabilities of all possible unique outcomes sum to 1 can be used to find unknown probabilities.
  4. 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.

Question 1 in Task A could be extended by asking pupils to think of other sets of events that have probabilities which sum to 1 because they are both mutually exclusive and exhaustive.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
A __________ diagram is a representation used to model statistical/probability questions, where branches represent different possible events or outcomes.
Correct Answer: tree, outcome tree
Q2.
What is the probability that the spinner lands on the number 2?
An image in a quiz
$${1}\over{2}$$
Correct answer: $${1}\over{3}$$
$${2}\over{3}$$
$${2}\over{6}$$
Q3.
What is the probability that the spinner does not land on the number 2?
An image in a quiz
$${1}\over{2}$$
$${1}\over{3}$$
Correct answer: $${2}\over{3}$$
$${2}\over{6}$$
Q4.
Which values represent the probability that this spinner lands on an integer?
An image in a quiz
$${1}\over{3}$$
Correct answer: 1
1%
Correct answer: 100%
Correct answer: $${3}\over{3}$$
Q5.
Based on the Venn diagram, which numbers belong to both sets A and B?
An image in a quiz
1
2
Correct answer: 3
Correct answer: 6
9
Q6.
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?
An image in a quiz
$${1}\over{7}$$
$${3}\over{7}$$
$${1}\over{10}$$
Correct answer: $${3}\over{10}$$
$${9}\over{10}$$

Exit quiz

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6 Questions

Q1.
Two or more events are __________ if they share no common outcome.
certain
exhaustive
impossible
likely
Correct answer: mutually exclusive
Q2.
A set of events are __________ if at least one of them has to occur whenever the experiment is carried out.
certain
Correct answer: exhaustive
impossible
likely
mutually exclusive
Q3.
A standard six-sided dice is rolled. Which pairs of events are mutually exclusive?
Correct answer: {odd, even}
{prime, even}
{factor of 6, multiple of 6}
Correct answer: {6, lower than 6}
Correct answer: {prime, square}
Q4.
A standard six-sided dice is rolled. Which pairs of events are exhaustive?
Correct answer: {odd, even}
{prime, even}
Correct answer: {factor of 6, multiple of 6}
Correct answer: {6, lower than 6}
{prime, square}
Q5.
When a set of events are all mutually exclusive and exhaustive, their probabilities sum to .
Correct Answer: 1, 100%, one, a whole, one whole
Q6.
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?
Correct Answer: 0.9, 0.90, 90%