Explain, by suitably defining events A and B, what is meant by 'the probability of A occurring given that B has occurred. A local greengrocer sells conventionally grown and organically grown vegetables. Conventionally grown vegetables constitute 80% of his sales; carrots constitute 12% of the conventional sales and 30% of the organic sales. Display this information in an appropriately and accurately labelled tree diagram. One day a customer emerges from the shop and is questioned about her purchases. What is the probability that she bought

(a) conventionally grown carrots,

(b) carrots? Given that she did buy carrots, what is the probability that they were organically grown? What assumptions have you made in answering this question?