# Marginal & Conditional Probability

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?

Please see attached problem.

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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

Answers

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.