Question

c) Suppose that 100 people are surveyed and it is found that 78 like oranges, 47 like mangoes
and 10 like neither. How many like both? How many like oranges but not mangoes?​

Answer 1

$\textbf{Given:}$

$\textsf{Suppose that 100 people are surveyed and it is found that}$

$\textsf{78 like oranges, 47 like mangoes and 10 like neither.}$

$\textbf{To find:}$

$\textsf{Number of people who like oranges but not mangoes}$

$\textbf{Solution:}$

$\underline{\textsf{Number of people who like atleast one of the fruits}}$

$\mathsf{=100-10}$

$\mathsf{=90}$

$\textsf{Let A and B be the set of people who like oranges and}$

$\textsf{B be the set people who like mangoes}$

$\textsf{As per given data,}$

$\mathsf{n(A)=78\;and\;n(B)=47}$

$\mathsf{n(A{\cup}B)=90}$

$\implies\mathsf{n(A)+n(B)-n(A{\cap}B)=90}$

$\implies\mathsf{78+47-n(A{\cap}B)=90}$

$\implies\mathsf{n(A{\cap}B)=125-90}$

$\implies\mathsf{n(A{\cap}B)=35}$

$\mathsf{Now,}$

$\underline{\textsf{Number of who like oranges but not mangoes}}$

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

$\mathsf{=n(A)-n(A{\cap}B)}$

$\mathsf{=78-35}$

$\mathsf{=43}$

$\textbf{Find more:}$

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