Answer :
Answer:
A) 0.32
Step-by-step explanation:
To determine the empirical conditional probability that a customer who ordered a chocolate-flavored cupcake also had it with cream cheese frosting, we need to calculate the value that should be in the cell of the provided two-way table for Chocolate and Cream Cheese Frosting.
Chocolate cupcake with Buttercream Frosting
To find the probability that a customer who ordered a chocolate-flavored cupcake had it with buttercream frosting, subtract the probability of having the vanilla cupcake with buttercream frosting from the total buttercream frosting probability:
[tex]\sf \;\;\;\;P(\textsf{Chocolate cupcake with Buttercream Frosting})\\\\= P(\textsf{Buttercream Frosting}) - P(\textsf{Vanilla cupcake with Buttercream Frosting}) \\\\= 0.60 - 0.12\\\\= 0.48\\\\[/tex]
Chocolate cupcake with Cream Cheese Frosting
To find the probability that a customer who ordered a chocolate-flavored cupcake had it with cream cheese frosting, subtract the probability of having a chocolate cupcake with buttercream frosting from the total probability of chocolate-flavored cupcakes:
[tex]\sf \;\;\;\;P(\textsf{Chocolate cupcake with Cream Cheese Frosting})\\\\= P(\textsf{Chocolate cupcake}) - P(\textsf{Chocolate cupcake with Buttercream Frosting}) \\\\= 0.80 - 0.48\\\\= 0.32[/tex]
Therefore, the empirical conditional probability that a customer who ordered a chocolate-flavored cupcake had it with cream cheese frosting is:
[tex]\LARGE\boxed{0.32}[/tex]