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# Probability

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A drawer contains 3 white balls and 6 black balls. Two balls are drawn out of the box at random. What is the probability that they both are black?

Dec 21, 2021

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We can either use combinations:

Since there are 6 black balls and we're choosing 2, and there are a total of 9 balls, we calculate $$\frac{6 \choose 2}{9 \choose 2}$$which is 15/36 or 5/12.

Or multiplication principle:

The probability that the first ball is black is 6/9 = 2/3. Since both the black and the total have been reduced by 1, the probability that the second ball and the first ball are black is 2/3 * 5/8 = 10/24 = 5/12.

Dec 21, 2021