weet Treats Company was interested in customers' orders. A population of customers was surveyed to determine the type of cupcake flavor and frosting flavor that was used. Given are the results of the survey in a two-way table.

Using this data, what is the empirical conditional probability that a customer who ordered a chocolate flavored cupcake had it with cream cheese frosting?
0.32
0.40
0.80
0.90

Question

24-06-2024
Mathematics

Answered

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weet Treats Company was interested in customers' orders. A population of customers was surveyed to determine the type of cupcake flavor and frosting flavor that was used. Given are the results of the survey in a two-way table.

Using this data, what is the empirical conditional probability that a customer who ordered a chocolate flavored cupcake had it with cream cheese frosting?
0.32
0.40
0.80
0.90

Sagot :

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semsee45 semsee45 · Answer 1 · 2024-06-24T05:18:06-04:00

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]

Sagot :

Chocolate cupcake with Buttercream Frosting

Chocolate cupcake with Cream Cheese Frosting

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