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? c p 10 4 8 3 u

Explanation:

Step1: Identify number of customers who like cake

The number of customers who like cake is the sum of those who like only - cake and those who like both cake and pie. So, \(n(C)=10 + 4=14\).

Step2: Identify number of customers who like both cake and pie

The number of customers who like both cake and pie is \(n(C\cap P)=4\).

Step3: Use the formula for conditional probability

The formula for conditional probability is \(P(P|C)=\frac{n(C\cap P)}{n(C)}\). Substituting the values we found, \(P(P|C)=\frac{4}{14}=\frac{2}{7}\).

Answer:

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