In a musical chair game, the person playing the music has been advised to stop playing the music anytime within three minutes after she starts playing. What is the probability that the music will stop within the first half minute after starting?

\frac{1}{6}

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\frac{2}{3}

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\frac{1}{4}

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\frac{1}{3}

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Solution

The correct option is A $\frac{1}{6}$
$T h e m u s i c c a n b e s t o p p e d a n y t i m e w i t h i n f i r s t 3 m i n u t e . T h e m u s i c c a n b e s t o p p e d w i t h i n a n y t i m e w i t h i n 3 m i n u t e . A s w e u n d e r s t a n d 3 m i n = 180 s e c i e t h e m u s i c c a n b e s t o p p e d a n y t i m e w i t h i n 180 s e c . I f t h e m u s i c h a s t o s t o p p e d w i t h i n f i r s t h a l f m i n u t e (i n c l u d i n g 1 / 2 m i n u t e b o u n d a r y) = w i t h i n 30 s e c, w e n e e d t o f i n d p r o b a b i l i t y o f t h i s 30 s e c w i t h i n 180 s e c . T h i s i s e v a l u a t e d a s p r o b a b i l i t y o f 30 s e c e v e n t w i t h i n 180 s e c = 30 / 180 = 1 / 6$

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