Probability Conditional Probability GCSE Statistics Probability Conditional Probability

When the probability of an event B happening depends on the outcome of a previous event A it is called conditional probability. We write the probability as P(B|A). for example, if you take a coloured ball from a bag of mixed colours then take another ball without replacing the first ball, the probability of getting a particular coloured ball depends on what colour the first ball was. If there were 3 red balls and 7 yellow balls in the bag and Karim chooses a red ball on his first turn then on his second turn the probability of a red ball is 2 9 (2 red balls left out of 9) and the probability of selecting a yellow ball would be 7 9 (7 red balls left out of the 9 balls). If Karim chooses a yellow ball on his first selection then the probability of a yellow ball for his second selection would be 7 9 and the probability of selecting a red ball on his second try would be 3 9 = 1 3 . This can be represented on a tree diagram . . . .

the total of these probabilities is 1 Y 3 10 7 10 ball 1 ball 2 3 9 6 9 P(R,R) = P(R,Y) = P(Y,R) = P(Y,Y) = probability 3 10 × 2 9 = 6 90 = 1 15 3 10 × 7 9 = 7 30 7 10 × 3 9 = 7 30 7 10 × 6 9 = 7 15 2 9 7 9 the total of these probabilities is 1 The probability of getting two balls the same colour P(R and R) + P(Y and Y) = 1 15 + 7 15 = 8 15 the probability of getting a red and a yellow ball would be: P(R and Y) + P(Y and R) = 7 30 + 7 30 = 7 15

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