Music is Life

Probability Level 2

A box contains music $CD's$ . Thirty are country music. Twenty are rock music. Thirty-five are pop music. Three $CD's$ are drawn at random from the box without replacement. Determine the probability that that all three $CD's$ are country music.

\dfrac{58}{1411}

\dfrac{85}{1411}

\dfrac{24360}{592630}

\dfrac{30}{85}

1 solution

A Former Brilliant Member
May 6, 2017

There are $30+20+35=85~CD's$ . The probability of randomly selecting a country music on the first draw is $\dfrac{30}{85}$ . There are now $29$ $CD's$ for country music in a batch of $84$ . The probability of randomly selecting a country music on the second draw is $\dfrac{29}{84}$ . There are now $28$ $CD's$ for country music in a batch of $83$ . The probability of randomly selecting a country music on the third draw is $\dfrac{28}{83}$ . Hence the probability of selecting a country music on the first draw and on the second draw and on the third draw is:

$\dfrac{30}{85}\times \dfrac{29}{84} \times \dfrac{28}{83}=\dfrac{24360}{592620}=\dfrac{58}{1411}$

Music is Life

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