Question

In a survey of a community of 48 people, it was found that 30 people liked product X, 25 people liked product Y and 30 liked product Z. If 17 people liked product X and Y, 15 people liked Y and Z, 14 people liked Z and X and 9 people liked all the three products. Then the number of people who like exactly one product, is (Given that each person like atleast one of the product X, Y or Z)


10


15


20


30

Answer 1

$\text{Let A,B and C be the set of peoples who like the}$

$\text{product X,Y and Z respectively}$

$\textbf{Given:}$

$n(A)=30$

$n(B)=25$

$n(C)=30$

$n(A{\cap}B)=17$

$n(B{\cap}C)=15$

$n(A{\cap}C)=14$

$n(A{\cap}B{\cap}C)=17$

$\textbf{To find:}$

$\text{The number of who like exactly one product}$

$\textbf{Solution:}$

$\textbf{Number of people who like only X}$

$=n(A{\cap}B\,'{\cap}C\,')$

$=n(A)-[n(A{\cap}B)+n(A{\cap}C)-n(A{\cap}B{\cap}C)]$

$=30-[17+14-9]$

$=30-22$

$=8$

$\textbf{Number of people who like only Y}$

$=n(A\,'{\cap}B{\cap}C\,')$

$=n(B)-[n(A{\cap}B)+n(B{\cap}C)-n(A{\cap}B{\cap}C)]$

$=25-[17+15-9]$

$=25-23$

$=2$

$\textbf{Number of people who like only Z}$

$=n(A\,'{\cap}B\,'{\cap}C)$

$=n(C)-[n(A{\cap}C)+n(B{\cap}C)-n(A{\cap}B{\cap}C)]$

$=30-[14+15-9]$

$=30-20$

$=10$

$\therefore\textbf{Number of people who like exactly one product is 8+2+10=20}$

Find more:

In a class 82 people were asked their favorite fruits ?39 likes apples, 50 liked bananas, 39 like pears, 21 liked apples and bananas, 18 liked bananas,

and pears, 19 liked apples and pears. How many liked all three types of fruits ?

https://brainly.in/question/16410523