Question

In Thimphu Primary School. 3/4 of the girls play basketball, 1/2 play badminton, 1/8 of those
who play badminton do not play basketball. How many girls play none of the games?​

Answer 1

0000000000000000000000000000000000

Answer 2

SOLUTION

GIVEN

In Thimphu Primary School.

• 3/4 of the girls play basketball
• 1/2 play badminton
• 1/8 of those who play badminton do not play basketball.

TO DETERMINE

The number of girls play none of the games

EVALUATION

Let total number of girls = x

Let

A = Set of girls who plays Basketball

B = Set of girls who plays Badminton

U = The set of all girls in the school ( Universal Set)

$\displaystyle \sf{}n(U) = x$

$\displaystyle \sf{}n(A) = \frac{3x}{4}$

$\displaystyle \sf{}n(B) = \frac{x}{2}$

Now 1/8 of those who play badminton do not play basketball.

$\displaystyle \sf{}n(A' \cap \: B) = \frac{x}{8}$

$\implies \: \displaystyle \sf{ n(B)\: - n(A \cap \: B) \: = \frac{x}{8} }$

$\implies \: \displaystyle \sf{ n(A \cap \: B) \: = \frac{x}{2} - \frac{x}{8} }$

$\implies \: \displaystyle \sf{ n(A \cap \: B) \: = \frac{3x}{8} }$

Now

$\displaystyle \sf{ n(A \cup \: B) \: }$

$= \displaystyle \sf{n(A ) + n(B) - n(A \cap \: B) \: }$

$= \displaystyle \sf{ \frac{3x}{4} + \frac{x}{2} - \frac{3x}{8} }$

$= \displaystyle \sf{ \frac{6x + 4x - 3x}{8} \: }$

$= \displaystyle \sf{ \frac{7x}{8} \: }$

So The number of girls play none of the games

$\sf{n(A' \cap \: B')}$

$= \sf{n(U) - n(A \cup \: B)}$

$\displaystyle \sf{} = x - \frac{7x}{8}$

$\displaystyle \sf{} = \frac{x}{8}$

FINAL ANSWER

$\displaystyle \sf{ \frac{1}{8} \: \: of \: girls \: play \: none \: of \: the \: games}$

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LEARN MORE FROM BRAINLY

If n(A) = 300, n(A∪B) = 500, n(A∩B) = 50

and n(B′) = 350, find n(B) and n(U).

https://brainly.in/question/4193770