Stephanie uses lots of ginger and chilli in her cooking. It turns out that: 75%

Question

Stephanie uses lots of ginger and chilli in her cooking. It turns out that: 75% of the meals prepared by Stephanie contain ginger; of the meals prepared by Stephanie containing ginger, 40% also contain chilli. (a) Let G denote the event that a meal prepared by Stephanie contains ginger, and let C denote the event that a meal prepared by Stephanie contains chilli. Write the information given in the two bullet points in symbolic form. (b) Calculate the probability that a randomly chosen meal prepared by Stephanie contains both ginger and chilli. (c) Additional information is now given that 50% of meals prepared by Stephanie contain chilli. Calculate the probability that a randomly chosen meal prepared by Stephanie that contains chilli also contains ginger. (d) What Percentage of meals prepared by Stephanie contain either ginger or chilli, or both? (e) For meals prepared by Stephanie, arc the events of containing ginger and containing chilli independent? Give a reason for your answer.

Explanation / Answer

a) P(G)=0.75

P(C|G)=0.40

b): P(G^U)=P(C|G)* P(G) = 0.40*0.75 = 0.3

c)P(C)=0.50

P(G|C)=P(G^U)/P(C) = 0.3/0.5 = 0.6

d) P(GUC) = P(G)+ P(C) - P(G^U)

= 0.75+0.50-0.3 = 0.95

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