Question

Suppose that, of all the customers at a coffee shop,70% purchase a cup of coffee;40% purchase a piece of cake;20% purchase both a cup of coffee and a piece of cake.Given that a randomly chosen customer has purchased a piece of cake, what is the probability that he/she has also purchased a cup of coffee

Answer 1

0.50

Explanation:

The probability that a customer has purchased a cup of coffee given that they have also purchased a piece of cake is determined by the percentage of customers who purchase both coffee and cake (20%) divided by the percentage of customers who purchase cake (40%):

`P(Coffee|Cake) = (P(Coffee\cap Cake))/(P(Cake))\\P(Coffee|Cake) =(0.20)/(0.40)=0.50`

50% of the customers also purchased coffee given that they have purchased a piece of cake.