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GCSE Mathematics › M5.2 Combined events and tree diagrams
Free AQA GCSE Mathematics practice questions on Combined events and tree diagrams. Sample questions below with detailed mark schemes — sign up to practise the full set with spaced repetition.
A student is investigating the reliability of a new type of light bulb. They test two bulbs independently. Each bulb has a probability of 0.8 of lasting longer than 1000 hours. The student wants to use a tree diagram to represent all possible outcomes.
A quality control manager at a manufacturing plant tests electronic components for defects. She randomly selects components and tests them twice independently. Each test has a probability of correctly identifying a defective component. The manager uses a tree diagram to calculate the probability that a component will pass both tests.
A bag contains 5 red counters and 3 blue counters. A counter is taken at random from the bag, its colour is recorded, and then it is replaced. A second counter is then taken at random from the bag.
A bag contains 4 green counters and 6 yellow counters. Mia takes a counter at random from the bag, notes its colour, and replaces it. She then takes a second counter at random. The tree diagram shows the possible outcomes.
A fair spinner has 4 equal sections numbered 1, 2, 3 and 4. The spinner is spun twice. The tree diagram below shows all possible outcomes.