Independent events
Objective. Multiply probabilities along independent branches.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Independent events are events where the outcome of one does not affect the probability of the other, such as flipping a coin twice or rolling two separate dice. For independent events, the probability of both happening together is found by multiplying their individual probabilities, written P(A and B) = P(A) × P(B). For example, the probability of rolling a 6 on a die and then flipping heads on a coin is (1/6) × (1/2) = 1/12, since the die roll does not influence the coin flip. Recognising independence is essential before applying this multiplication rule, since dependent events require adjusted probabilities for the second event.
Worked example
A fair coin is flipped and a fair six-sided die is rolled. Find the probability of getting tails on the coin and a 4 on the die, as these are independent events.
- 1Identify the individual probabilities: P(tails) = 1/2 and P(4) = 1/6.
- 2Since the events are independent, multiply the probabilities.
- 3Substitute: 1/2 × 1/6.
- 41/2 × 1/6 = 1/12.
Answer: 1/12
Concept mastery
Based on your past attempts at this lesson — the question types to practise again come first.
Complete a practice set to see your concept breakdown here.
Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. Pupils sometimes add the probabilities of two independent events instead of multiplying them, treating the combined 'and' event the same as an 'or' event. Always multiply probabilities for independent events occurring together.
Your progress
Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.
0 of 5 steps complete
Your place saves automatically as you read.