In a musical chair game, the person playing the music has been advised to stop playing the music at any time within 1.5 minutes after he starts playing. What is the probability that the music will stop within the first 15 seconds after starting?

The music can stop at any time within 1.5 minutes after starting. The probability needs to be found that the music stops within the first 15 seconds.

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Total time: 1.5 minutes

$1.5 \times 60 = 90$ seconds

First 15 seconds = 15 seconds

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The music stops at any time within 90 seconds with equal probability (uniform probability).

Probability $= \dfrac{\text{Time interval of interest}}{\text{Total time available}}$

Probability $= \dfrac{15}{90}$

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$\dfrac{15}{90} = \dfrac{15 \div 15}{90 \div 15}$

$= \dfrac{1}{6}$

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Therefore, the probability that the music will stop within the first 15 seconds is $\dfrac{1}{6}$.