Probability
Probability measures how likely an event is to happen, given as a number from 0 (impossible) to 1 (certain), written as a fraction, decimal or percentage. This GCSE Probability topic covers single and combined events using sample space diagrams, tree diagrams, two-way tables and Venn diagrams, since all probabilities in a situation must add up to 1.
Method
- Identify all the possible outcomes and check whether they are equally likely.
- For a single event, probability = number of favourable outcomes divided by total number of outcomes.
- Remember all probabilities for a set of mutually exclusive, exhaustive outcomes must add up to 1, so a missing probability can be found by subtracting the others from 1.
- For combined events, use a sample space diagram, two-way table, tree diagram or Venn diagram to organise the outcomes systematically.
- For independent events, multiply the probabilities along the branches of a tree diagram; for 'at least one', use 1 minus the probability of neither happening.
- Check your final probability is between 0 and 1.
Worked example
A bag contains only red, blue and yellow counters. A counter is picked at random. P(red) = 0.3 and P(blue) = 0.45. There are 60 counters in the bag. Work out the number of yellow counters.
- All probabilities must add up to 1, so P(yellow) = 1 - 0.3 - 0.45.
- P(yellow) = 0.25.
- Number of yellow counters = 0.25 x 60.
- Final answer: 15 yellow counters.
Practice questions
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Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
A spinner can land on red, blue or green. The table shows the probability of each colour in terms of x: red = 3x, blue = 2x, green = 5x. Work out the value of x, then work out P(blue).
A biased coin has P(Heads) = 0.7. The coin is flipped twice. (a) Find the probability that the coin lands on tails both times. (b) Find the probability that the coin lands on exactly one head.
A bag contains 9 counters: 5 red and 4 blue. Two counters are taken from the bag at random, without replacement. (a) Write down the four missing probabilities for a tree diagram showing this information. (b) Find the probability that both counters are the same colour.
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