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# Marginal & Conditional Probability

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2. For a marketing survey, 200 customers were classified according to their age (in years) and their favorite type of donut.
Age of Customer Glazed Chocolate-covered Crème-filled Cake
<21 3 25 10 7
21-30 5 23 26 10
31-45 15 12 3 20
>45 29 5 1 6
(a) What is the probability that a person prefers Creme-filled donut and is age 30 years or less?
(b) What is the probability that either a person's favorite donut is glazed or that the person is less than 21 year of age?
(c) What is the probability that a person is between 21 and 30 years of age if that person favors chocolate-covered donuts?
(d) Are age and favorite donut independent variables? Why or why not?

https://brainmass.com/math/probability/marginal-conditional-probability-marketing-survey-346221

#### Solution Preview

2. For a marketing survey, 200 customers were classified according to their age (in years) and their favorite type of donut.

Age of Customer Glazed Chocolate-covered Crème-filled Cake
<21 3 25 10 7
21-30 5 23 26 10
31-45 15 12 3 20
>45 29 5 1 6

Age of Customer Glazed Chocolate-covered Crème-filled Cake Total
<21 3 25 10 7 45
21-30 5 23 26 10 64
31-45 15 12 3 20 50
>45 29 5 1 6 41
Total 52 65 40 43 200

(a) What is the probability that a person prefers Creme-filled donut and is age 30 years or less?

There are 10 + 26 = 36 persons prefers Creme-filled donut and age 30 years or less. Total number of persons = 200. Therefore,

P (a ...

#### Solution Summary

The solution provides step by step method for the calculation of probabilities and conditional probabilities. Formula for the calculation and Interpretations of the results are also included.

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