Donato’s completed a marketing study to determine what types of pizza people lik
ID: 3270735 • Letter: D
Question
Donato’s completed a marketing study to determine what types of pizza people liked. They offered one free slice as their choice from cheese, meat lover and veggie to each of 1000 people and recorded their preference and their ages. The following table summarizes the results.
Age
25-34
35-44
45-65
Totals
Cheese
230
140
30
400
Meat
120
150
60
330
Veggie
50
60
160
270
Totals
400
350
250
If one person is chosen at random from the above study, determine the following:
(Give your answer as a fraction and a decimal rounded to three decimal places)
What is the probability that the person is 35-44 years old?
What is the probability that the person prefers cheese?
What is the probability that the person does NOT prefer veggie?
What is the probability that the person is 25-34 years old OR prefers cheese?
What is the probability that the person is 25-34 years old AND prefers veggie?
What is the probability that the person is 45-65 years old OR prefers cheese?
What is the probability that the person prefers cheese OR meat?
What is the probability that the person’s age is at least 34?
What is the probability that the person prefers meat AND veggie?
What is the probability that the person is 35-44 years old, given that the person prefers meat?
What is the probability that the person prefers meat, given that the person 35-44 years old?
What is the probability that the person is 35-44 years old AND prefers meat?
What is the probability that the person prefers veggie, given that the person is 25-34 years old?
What is the probability that the person is 25-34 years old, given that the person prefers veggie?
Is the preference independent of age? Use probabilities from above to demonstrate your decision.
Give an example of two events that are disjoint (mutually exclusive)?
Age
25-34
35-44
45-65
Totals
Cheese
230
140
30
400
Meat
120
150
60
330
Veggie
50
60
160
270
Totals
400
350
250
Explanation / Answer
Solution:-
1) The probability that the person is 35-44 years old is 0.35
Number of persons of age 35-44 years old = 350
Total number of persons = 1000
The probability that the person is 35-44 years old = 350/1000 = 0.35
2) The probability that the person prefers cheese is 0.40.
Number of person who prefer chesse = 400
Total number of persons = 1000
The probability that the person prefers cheese = 400/1000 = 0.40
3) The probability that the person does NOT prefer veggie is 0.73.
Number of person who does NOT prefer veggie = 730
Total number of persons = 1000
The probability that the person does NOT prefer veggie = 730/1000 = 0.73
4) The probability that the person is 25-34 years old OR prefers cheese is 0.57.
The number of person who are 25-34 years old OR prefers cheese = 400 + 400 - 230 = 570
Total number of persons = 1000
The probability that the person is 25-34 years old OR prefers cheese = 570/1000 = 0.57
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