Suppose a bag contains 4 white chips and 6 black chips. What is the probability of randomly choosing a white chip, not replacing it, and then randomly choosing another white chip?

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Jun 16, 2016

$\frac{2}{15}$

Explanation:

There are initially $4 + 6 = 10$ chips in the bag, so the probability of the first chip drawn being white is:

$\frac{4}{10} = \frac{2}{5}$

Having drawn a white chip there are then $3$ white chips left in the bag out of a total $3 + 6 = 9$ chips. So the probability of the second chip also being white is:

$\frac{3}{9} = \frac{1}{3}$

So the probability of drawing two white chips is:

$\frac{2}{5} \cdot \frac{1}{3} = \frac{2}{15}$

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