Question

twenty - five bakery customers were surveyed to determine if they like cake or pie. the results are shown in the venn diagram. given that a randomly chosen customer likes cake, what is the probability that the customer also likes pie? 2/7 2/5 4/7 4/5

Explanation:

Step1: Calculate the number of customers who like cake

The number of customers who like cake is \(10 + 4=14\) (the part of the cake - only circle \(10\) plus the intersection \(4\)).

Step2: Calculate the probability

The number of customers who like both cake and pie is \(4\). Using the formula for conditional probability \(P(Pie|Cake)=\frac{n(Cake\cap Pie)}{n(Cake)}\), we substitute \(n(Cake\cap Pie) = 4\) and \(n(Cake)=14\). So \(P=\frac{4}{14}=\frac{2}{7}\)

Answer:

\(\frac{2}{7}\)