Probability-Formulae gcse Edexcel

Addition Law & Mutually Exclusive Events

What are mutually exclusive events?

• Two events are mutually exclusive if they cannot both occur at the same time

  • e.g. ‘get an even number’ and ‘get an odd number’ are mutually exclusive when rolling a dice

  • ‘get an even number’ and ‘get a multiple of 3’ are not mutually exclusive

    • 6 is both an even number and a multiple of 3

• If two events are mutually exclusive you can add their probabilities to find the probability of one or the other happening

  • If events A and B are mutually exclusive,

    • then

  • This is known as the addition law for two mutually exclusive events

    • But it is often referred to as the ‘or’ rule

What are exhaustive events?

• A set of events is called exhaustive if all possible outcomes are included in the set

  • e.g. ‘heads’ and ‘tails’ is an exhaustive set for flipping a coin

  • ‘get an even number’ and ‘get an odd number’ is an exhaustive set for rolling a 6-sided dice

    • but so is ‘get a 1’, ‘get a 2’, etc., up to ‘get a 6’

• For an exhaustive set of mutually exclusive events, the sum of all probabilities is equal to 1

  • e.g. for flipping a coin

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