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?

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?

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, $10 + 4=14$.

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 4.

Step3: Calculate the conditional probability

The formula for conditional probability $P(Pie|Cake)=\frac{P(Cake\cap Pie)}{P(Cake)}$. In terms of counts, $P(Pie|Cake)=\frac{\text{Number of customers who like both}}{\text{Number of customers who like cake}}=\frac{4}{14}=\frac{2}{7}$.

Answer:

$\frac{2}{7}$