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?\no $\frac{2}{7}$\no $\frac{2}{5}$\no $\frac{4}{7}$\no $\frac{4}{5}$

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?\no $\frac{2}{7}$\no $\frac{2}{5}$\no $\frac{4}{7}$\no $\frac{4}{5}$

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

From the Venn - diagram, (n(C\cap P)=4).

Step3: Use the formula for conditional probability

The formula for conditional probability is (P(P|C)=\frac{P(C\cap P)}{P(C)}). Since (P(C\cap P)=\frac{n(C\cap P)}{n(U)}) and (P(C)=\frac{n(C)}{n(U)}), then (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})