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3) Consider a marketing application. There are three styles of a certain product. Of the consumers buying this product 32% purchase style 1, 54% purchase style 2, and the rest purchase style 3. Given that the costumers' purchases style 1, 65% are buying it as a gift, while 87% of customers known to purchase style 2 buy it as a gift, and 19% of the customers known to purchase style 3 are purchasing it as a gift. a) What is the probability an individual is purchasing the product as a gift? b) What is the probability the customer purchases style 2 and it is a gift? What is the probability the customer purchases style 2 given that they came in to the store to buy a gift?

3) Consider a marketing application. There are three styles of a certain product. Of the consumers buying this product 32% purchase style 1, 54% purchase style 2, and the rest purchase style 3. Given that the costumers' purchases style 1, 65% are buying it as a gift, while 87% of customers known to purchase style 2 buy it as a gift, and 19% of the customers known to purchase style 3 are purchasing it as a gift. a) What is the probability an individual is purchasing the product as a gift? b) What is the probability the customer purchases style 2 and it is a gift? What is the probability the customer purchases style 2 given that they came in to the store to buy a gift?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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3) Consider a marketing application. There are three styles of a certain product. Of the consumers buying this product 32% purchase style 1, 54% purchase style 2, and the rest purchase style 3. Given that the costumers' purchases style 1, 65% are buying it as a gift, while 87% of customers known to purchase style 2 buy it as a gift, and 19% of the customers known to purchase style 3 are purchasing it as a gift. a) What is the probability an individual is purchasing the product as a gift? b) What is the probability the customer purchases style 2 and it is a gift? What is the probability the customer purchases style 2 given that they came in to the store to buy a gift?
Transcribed Image Text:3) Consider a marketing application. There are three styles of a certain product. Of the consumers buying this product 32% purchase style 1, 54% purchase style 2, and the rest purchase style 3. Given that the costumers' purchases style 1, 65% are buying it as a gift, while 87% of customers known to purchase style 2 buy it as a gift, and 19% of the customers known to purchase style 3 are purchasing it as a gift. a) What is the probability an individual is purchasing the product as a gift? b) What is the probability the customer purchases style 2 and it is a gift? What is the probability the customer purchases style 2 given that they came in to the store to buy a gift?
Expert Solution
Step 1

Define the Events,

S1 :  Person purchases style 1

S2 : Person purchases style 2

S3 : Person purchases style 3

X : buying the product as a gift.

Given, 32% purchases style 1. 54% purchases style 2, rest (100-32-54) % = 14% purchases style 3.

So, P(S1) = 0.32, P(S2) = 0.54, P(S3) = 0.14

65% of style 1 purchased as a gift, 87% of the style 2 purchased as gift and 19% of the style 3 purchased as gift.

So, P(X|S1) = 0.65, P(X|S2) = 0.87, P(X|S3) = 0.19

a. To find, 

P( an individual is purchasing the product as a gift)

= P(X)

= P(X|S1)P(S1) + P(X|S2)P(S2) + P(X|S3)P(S3)

=0.65*0.32 + 0.87*0.54+0.14*0.19

=0.7044

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