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Question Number 7969 by tawakalitu last updated on 26/Sep/16

D u r i n g o n e y e a r i n a s c h o o l, \frac{5}{8} o f t h e s t u d e n t s

h a d m e a s i l e s . \frac{1}{2} h a d c h i c k e n p o x, a n d \frac{1}{8} h a d

N e i t h e r . W h a t f r a c t i o n o f t h e s c h o o l h a d b o t h

m e a s i l e s a n d c h i c k e n p o x .

Answered by Rasheed Soomro last updated on 26/Sep/16

L e t t h e f r a c t i o n o f t h e s c h o o l

w h o h a v e b o t h d i s e a s e s i s x

f r a c t i o n o f, w h o h a v e o n l y m e a s i l e s = \frac{5}{8} - x

f r a c t i o n o f, w h o h a v e o n l y c h i c k e n p o x = \frac{1}{2} - x

(H a v i n g o n l y m e a s i l e s) + (H a v i n g o n l y c h i c k e n p o x)

+ (H a v i n g b o t h) + (H a v i n g n e i t h e r) = 1 (W h o l e)

(\frac{5}{8} - x) + x + (\frac{1}{2} - x) + \frac{1}{8} = 1

\frac{5}{8} + \frac{1}{2} + \frac{1}{8} - x = 1

x = \frac{5}{8} + \frac{1}{2} + \frac{1}{8} - 1 = \frac{5 + 4 + 1 - 8}{8} = \frac{2}{8} = \frac{1}{4}

Commented by tawakalitu last updated on 26/Sep/16

T h a n k s s o m u c h s i r . G o d b l e s s y o u .

Answered by sandy_suhendra last updated on 26/Sep/16

a n o t h e r a n s w e r :

t h e s t u d e n t s h a d m e a s i l e s = n (M) = \frac{5}{8}

t h e s t u d e n t s h a d c h i c k e n p o x = n (C) = \frac{1}{2}

n (M \cup C) = n (M) + n (C) - n (M \cap C)

1 - \frac{1}{8} = \frac{5}{8} + \frac{1}{2} - n (M \cap C)

\frac{7}{8} = \frac{9}{8} - n (M \cap C)

s o h a d b o t h m e a s i l e s a n d c h i c k e n p o x = n (M \cap C) = \frac{2}{8} = \frac{1}{4}

Commented by tawakalitu last updated on 26/Sep/16

I r e a l l a p p r e c i a t e s i r . G o d b l e s s y o u .