Sum of probabilities - KS3 Maths

Key points

An image of a single decker bus. Written below. P, open bracket, late, close bracket, equals zero point zero four. Written beneath. P, open bracket, not late, close bracket, equals question mark. — Image caption,
It is certain that this bus will either be late or not late, which is a probability of 1

A is how likely something is. The of the probabilities of all the possible is 1. One of the outcomes will definitely happen.
The probability of something happening and the probability of it not happening add up to one. It is certain that an will either happen or not happen, and that is a probability of 1.
The missing value of a probability can be worked out by subtracting the known probabilities from 1 (100% when working in percentages). The calculations may involve fractions, decimals or percentages.
When adding and subtracting probabilities to calculate unknown probability values, it is helpful to be able to add and subtract fractions and decimals.

Use the fact that the sum of probabilities of an event is 1

To find a missing probability value:

Add up the given probabilities.
Subtract the total of the probabilities from 1 (100% when working in percentages).

To add and subtract fractions, use a .

Examples

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A bag only contains blue, orange and green counters. A counter is taken at random from the bag. P(blue) = 0۰25, P(orange) = 0۰3. Work out P(green).
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P(green) is the sum of the known probabilities subtracted from 1. Sum the given probabilities. P(blue) + P(orange) = 0۰55
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Subtract 0۰55, the sum of the known probabilities, from 1. 1 – 0۰55 = 0۰45. P (green) = 0۰45
$Example two, working in fractions. An image of a punnet of mixed fruit, made up of raspberries, blueberries, and cherries. Written below. P, open bracket, raspberry, close bracket, equals one tenth. P, open bracket, blueberry, close bracket, equals three fifths. P, open bracket, cherry, close bracket, equals question mark.$
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A punnet contains raspberries, blueberries and cherries. One berry is picked out of the punnet at random. P(raspberry) = ⅒, P(blueberry) = ⅗. Find the probability of picking a cherry from the punnet, P(cherry).
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P(cherry) is the sum of the known probabilities subtracted from 1. Sum the given probabilities, P(raspberry) + P(blueberry). The highest common factor (HCF) of 5 and 10 is the common denominator used to add the fractions. The equivalent fraction for ⅗ is ⁶⁄₁₀. The fraction 1⁄₁₀ does not change, the denominator is already 10. The sum of 1⁄₁₀ and ⁶⁄₁₀ is 7⁄₁₀.
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Subtract 7⁄₁₀, the sum of the known probabilities, from 1. P(cherry) = 3⁄₁₀.
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A spinner is coloured orange, blue, green and black. The table shows the probability of a spinner landing on each colour. Find the probability of the spinner landing on blue.
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P(blue) is the sum of the known probabilities subtracted from 100%. Sum the given probabilities. P(orange) + P(green) + P(black) = 70%.
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Subtract 70%, the sum of the known probabilities, from 100%. P(blue) = 30%.

Question

A raffle ticket may be purple, blue or green.

The probability of a purple ticket is $ \frac{2}{5}$.

The probability of a blue raffle ticket is $ \frac{1}{4}$.

Find the probability of a green raffle ticket.

P, open bracket, purple, close bracket, equals two fifths. P, open bracket, blue, close bracket, equals one quarter. P, open bracket, green, close bracket, equals question mark.

Calculate the probability that an event does not happen

The of an happening and the probability of the same event not happening sum to 1. It is certain that the event will either happen or not happen.
To find probability that an event does not happen.
- Subtract the P(event) from 1
The calculation may involve a fraction, decimal or percentage.

Examples

Skip image gallery

Image caption,
The probability of an event happening and the probability of the same event not happening sum to 1. It is certain that the event will either happen or not happen.
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The probability of an event not happening is the probability of the event happening subtracted from 1
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If the probability of a bus being late is 0۰04, find the probability that the bus is not late.
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To find the probability that the bus is not late, subtract P(late) from 1. P(not late) = 0۰96
$Example three. Working with fractions A series of three images. Each image shows a person performing a different exercise. The first image is labelled, squat, and shows a person performing a squat. The second image is labelled, lunge, and shows a person performing a lunge. The third image is labelled, plank, and shows a person performing a plank. Written below: P, open bracket, squat, close bracket, equals three eighths. P, open bracket, not a squat, close bracket, equals question mark.$
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A training session is made up of three exercises: squats, lunges and planks. The probability that the exercise is a squat is ⅜. Find the probability that the exercise is not a squat.
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To find the probability that the movement is not a squat, subtract P(squat) from 1. P(not a squat) = ⅝. It is not necessary to know the probability of the other movements to work this out.

Question

The probability that it will rain is $ \frac{1}{5}$.

What is the probability that it will not rain?

P, open bracket, rain, close bracket, equals one fifth. P, open bracket, not rain, close bracket, equals question mark.

Practise finding the sum of probabilities

Practise working out the sum of probabilities with this quiz. You may need a pen and paper to help you with your answers.

Quiz

Real-life maths

An image of a weather app on a phone. — Image caption,
People often use a weather app to find out the probability of rain in a particular area.

A meteorologist studies the weather, working with data to assess how likely it is that there will be rain, snow, wind or sun on a given day in a particular area. People use the information given by meteorologists, such as on a weather app, to make decisions when planning activities.

For example, if the probability of rain is 10%, then the probability of no rain is 90%, meaning doing something outdoors could be more appealing. If the probability of rain is 70%, this could put people off, making them decide to stay indoors instead.