AQA•GCSE•Mathematics•Probability
Independent events
AQA GCSE Mathematics practice questions with step-by-step solutions
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Sample Questions
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EasyQuestion 1
[2 marks]Two fair coins are flipped independently.
Find the probability of getting a head on both coins.
Solution for Question 1
MediumQuestion 2
[3 marks]A dice is rolled and a card is drawn from a standard pack.
Find the probability of:
(a) rolling a 6 AND drawing an ace
(b) rolling an even number AND drawing a heart
Solution for Question 2
HardQuestion 3
[4 marks]A machine has a 0.02 probability of producing a faulty item. Three items are produced independently.
Find the probability that:
(a) all three are faulty
(b) none are faulty
(c) at least one is faulty
Solution for Question 3
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Generate Unlimited QuestionsAbout Independent events in AQA GCSE
Events are independent if one happening doesn't affect the probability of the other. Coin flips are independent - getting heads doesn't change the probability of the next flip. Drawing with replacement is independent; drawing without replacement is dependent.
For independent events: P(A and B) = P(A) × P(B). This multiplication rule extends to any number of independent events. Simply multiply all the individual probabilities.
Be careful to check independence. If items are selected "without replacement" or one event changes the conditions for another, the events are dependent and require different methods (like adjusted tree diagrams).
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