twenty - five bakery customers were surveyed to determine if they like cake or pie. the results are shown in…

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? o $\frac{2}{7}$ o $\frac{2}{5}$ o $\frac{4}{7}$ o $\frac{4}{5}$
Answer
Explanation:
Step1: Find 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: Find 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 conditional - probability formula
The formula for conditional probability is (P(P|C)=\frac{P(C\cap P)}{P(C)}). In terms of counts, (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})