Combined Probability (AQA GCSE Maths): Revision Note

Combined Probability

How do I calculate combined probabilities?

• You can calculate probabilities of one event after another without needing tree diagrams

  • These are called combined (or successive) probabilities

• There are two rules to learn

  • And means multiply and or means add

  • P(A and B) = P(A) x P(B)

  • P(AA or BB) = P(AA) + P(BB)

• Try to rephrase each question using and / or

  • For example, when flipping a coin twice: 

    • P(two heads) = P(head and head)

    • P(both the same) = P(head and head or tail and tail) = P(HH) + P(TT)

• Remember that P(not A) = 1 - P(A)

What does independent mean?

• Independent events are events that do not affect each other

  • e.g. the probability of rolling a 6 on a fair dice and the probability of getting a head when flipping a coin

• Be careful: questions 'without replacement' are not independent

  • e.g. the probability of taking a red card out of a pack, not replacing it, then finding the probability of taking a second red card out of the same pack

    • The first event affected the number of cards left for the second event