Probability Mutually exclusive and exhaustive events GCSE Statistics Probability Mutually exclusive and exhaustive events

Mutually exclusive events (7.7) Events are mutually exclusive if they can not happen at the same time. A coin that is flipped can not come down heads and tails at the same time so the events ‘a head’ and ‘a tail’ are mutually exclusive. If two events A and B are mutually exclusive P( A or B) = P(A) + P(B) This is called the addition for mutually exclusive events For example, if the probability of A hitting a six off the last ball of a cricket match is 0.03 and the probability of B hitting or running a four off the last ball is 0.08 and four runs are needed to win the game, the probability of winning = P(A) + P(B) = 0.03 + 0.08 =0.11 The law may be extended to three or more events: P(A or B or C) = P(A) + P(B) + P(C)

We write this as P(A) + P(not A) = 1 Exhaustive events (7.8 – 7.9) A set of events is exhaustive if the set contains all possible outcomes. For a set of exhaustive events, the sum of the probabilities is one (∑p = 1) In particular the probability of an event happening + the probability of an event not happening = 1 We write this as P(A) + P(not A) = 1 For example, if a bag contains red yellow and green balls and the probability of getting a red ball is 0.4, the probability of getting yellow or green ball = P(not red) = 1 – 0.4 = 0.6

Independent events and the multiplication law (7.10) Two events are independent if the outcomes of one event does not effect the outcome of the other. For two independent events A and B, the P(A and B) = P(A) x P(B) This is called the multiplication law for independent events.

Your turn Exercise 7H page 273 Exercise 7I page 275