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)

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 7 H page 273 Exercise 7 I page 275