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? c p 10 4 8 3 u

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

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, 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 $P(P|C)=\frac{n(C\cap P)}{n(C)}$. Substituting the values we found, we get $P(P|C)=\frac{4}{14}=\frac{2}{7}$.

Answer:

$\frac{2}{7}$