Chapter 6.2, Problem 40E

BRAND SWITCHING AMONG FEMALE COLLEGE STUDENTS In a survey of factors that influence brand switching by $18$- to $24$- year-old female college students, the following factors were identified as being significant as judged by the responses of the $439$ participants in the survey:

1: Better price

2: Friend’s recommendation

3: Seeing others use it

4: Intersting packaging

5: Buzz-people talking about the brand

6: An advertisement

7: Press stories

8: Entertainer/sports celebrity endorsement

The results of the survey follow:

Factor	1	2	3	4	5	6	7	8
Respondents (%)	$68.8$	$60.4$	$22.8$	$20.8$	$16.8$	$16.8$	$14.9$	$6.9$

Let $A$ denote the set of factors that had a response greater than $20\%$, let $B$ denote the set of factors that had a response between $15\%$ and $25\%$, and let $C$ denote the set of factors that had a response less than $25\%$. Find:

a. $n\left(A\right),n\left(B\right),n\left(C\right)$	b. $n\left(A\cap B\right)$	c. $n\left(A^C\cap C\right)$
d. $n\left(A\cap B^C\right)$	e. $n\left(A^C\cap C^C\right)$	f. $n\left[\left(A\cup B\right)\cap C\right]$

Source:Burst Media Research.