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A bag has 4 marbles, 5 white marbles, and 6 blue marbles. Three marbles are drawn from the bag (without replacement). What is the probability that they are all the same color?

 Jan 21, 2023
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There are two possibilities for all marbles drawn to be the same color: all white or all blue. The probability of drawing 3 white marbles out of 5 white marbles is (5C3) * (1/2)^3. The probability of drawing 3 blue marbles out of 6 blue marbles is (6C3) * (1/2)^3. The total probability of drawing 3 marbles of the same color is (5C3)*(1/2)^3 + (6C3)*(1/2)^3 = 2/11.

 Jan 21, 2023

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