A bag of 35 marbles contains equal amounts of the colors: blue, green, red, yellow, black, white, and orange. You draw 3 marbles without replacing them in the bag. What is the probability that all the marbles are blue? Give your answer as an exact fraction and reduce the fraction as much as possible

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23-10-2019
Mathematics

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A bag of 35 marbles contains equal amounts of the colors: blue, green, red, yellow, black, white, and orange. You draw 3 marbles without replacing them in the bag. What is the probability that all the marbles are blue? Give your answer as an exact fraction and reduce the fraction as much as possible

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allstarpitcher923 allstarpitcher923 · Answer 1 · 2019-10-23T08:05:23+02:00

There are 7 colors, so the probability of drawing any color is 1/5 on the first draw. After the first draw, there are 34 marbles left, and 4 blue marbles left. So the probability of drawing a blue marble on the second draw is 4/34 or 2/17. After the second draw, there are 33 marbles left and 3 blue marbles left. The probability of drawing a blue marble on the third draw is 3/33 or 1/11. The total probability of drawing 3 marbles in a row is (1/5) * (2/17) * (1/11) which is equal 2/935.