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13.1 Calculating Probability

GCSE Maths Foundation · Edexcel · Chapter 13: Probability

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: the probability scale, equally likely outcomes, “not” events and probability tables. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Describe how likely an event is in words and place it on the probability scale from 0 to 1
  • Work out the probability of an event when all outcomes are equally likely
  • Use the fact that P(not A) = 1 − P(A)
  • Use the fact that the probabilities of mutually exclusive outcomes add up to 1, including in tables

Key words

  • Event: Something that may happen, for example “the spinner lands on blue”.
  • Outcome: One possible result. Rolling a dice has 6 outcomes: 1, 2, 3, 4, 5, 6.
  • Equally likely: Every outcome has the same chance, as with a fair coin, a fair dice or a counter picked at random.
  • Probability: A number from 0 (impossible) to 1 (certain) that says how likely an event is. Write it as a fraction, decimal or percentage.
  • Mutually exclusive: Events that cannot happen at the same time, such as “lands on red” and “lands on blue” on one spin.

The probability scale

Every probability lies between 0 and 1. The closer to 1, the more likely the event. A probability can never be negative or bigger than 1.

Worked example: choosing the right word

A bag holds 9 green counters and 1 yellow counter. One counter is picked at random.
Picking green: 9 out of 10, so it is likely. Picking yellow: 1 out of 10, so it is unlikely. Picking blue: there are none, so it is impossible.

Answer: likely, unlikely, impossible

Equally likely outcomes

When all the outcomes are equally likely, count them.

Key fact: P(event) = number of outcomes in the event ÷ total number of outcomes

Worked example: a bag of counters

A bag holds 5 red, 3 green and 4 yellow counters. One is taken at random.
Total = 5 + 3 + 4 = 12. P(green) = 3/12 = 1/4.
P(red or yellow) = (5 + 4)/12 = 9/12 = 3/4.

Answer: P(green) = 1/4, P(red or yellow) = 3/4

Worked example: a fair spinner

Find P(prime number) on the spinner above.
The primes are 2, 3, 5 and 7: that is 4 of the 8 equal sections.
P(prime) = 4/8 = 1/2.

Answer: 1/2

The probability that an event does not happen

An event either happens or it does not, so the two probabilities add up to 1.

Key fact: P(not A) = 1 − P(A)

Worked example: rain tomorrow

The probability that it rains tomorrow is 0.35. Find the probability that it does not rain.
P(not rain) = 1 − 0.35 = 0.65.

Answer: 0.65

This works for fractions and percentages too: if P(win) = 2/9, then P(not win) = 7/9; if P(late) = 12%, then P(not late) = 88%.

Mutually exclusive outcomes and probability tables

On one spin a spinner can only land on one colour, so the colours are mutually exclusive. The probabilities of all the possible outcomes add up to 1.

Key fact: For mutually exclusive events, P(A or B) = P(A) + P(B).

  • Probability; Red 0.3; Blue 0.24; Green x; Yellow x

Worked example: a biased spinner

The table shows the probabilities for a biased spinner. Green and yellow are equally likely. Find x, then P(red or blue).
0.3 + 0.24 = 0.54, so green and yellow share 1 − 0.54 = 0.46.
2x = 0.46, so x = 0.23.
P(red or blue) = 0.3 + 0.24 = 0.54.

Answer: x = 0.23, P(red or blue) = 0.54

Working backwards to find a number of items

If you know the probability and the total, multiply to find how many items there are.

Worked example: a tin of biscuits

A tin holds 40 biscuits: plain, chocolate and ginger. P(plain) = 0.45 and P(chocolate) = 0.3. How many ginger biscuits are there?
P(ginger) = 1 − 0.45 − 0.3 = 0.25.
Number of ginger = 0.25 × 40 = 10.

Answer: 10 ginger biscuits

Common mistakes

  • Giving a probability bigger than 1 or less than 0. Check every answer is between 0 and 1.
  • Writing a probability as a ratio such as 3 : 12. Write a fraction, decimal or percentage: 3/12 = 1/4.
  • Assuming outcomes are equally likely when they are not. Win, draw and lose are 3 outcomes, but each is not 1/3.
  • Forgetting that the probabilities in a table must add up to exactly 1.

Revision questions

Try these, then check your answers below each one.

Question 1. A fair six-sided dice is rolled. Which word best describes the probability of rolling a number less than 7? (Choose from: Impossible, Unlikely, Even chance, Certain.)

Answer: Certain

Working: Every score 1 to 6 is less than 7, so the probability is 1: certain.

Question 2. A bag holds 6 blue, 5 red and 9 green counters. One counter is taken at random. Work out P(red) as a decimal.

Answer: 0.25

Working: Total = 6 + 5 + 9 = 20. P(red) = 5/20 = 0.25.

Question 3. A fair spinner is numbered 1 to 10. Work out the probability that it lands on a square number. Give a fraction.

Answer: 3/10

Working: Square numbers: 1, 4, 9. P = 3/10.

Related lessons

Continue in the full course

This lesson is section 13.1 (EGCMF1301) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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