Find the probability

Probability Level 1

A box contains 10 10 red marbles, 20 20 white marbles, 10 10 blue marbles, 5 5 green marbles, 15 15 indigo marbles, and 25 25 yellow marbles. One marble is drawn at random without replacement. Then another marble is drawn at random. What is the probability that the two marbles drawn are both indigo?

3 17 \frac{3}{17} 1 34 \frac{1}{34} 2 85 \frac{2}{85} 2 15 \frac{2}{15}

A Former Brilliant Member by A Former Brilliant Member

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1 solution

The total number of marbles is 85 85 and there are 15 15 indigo marbles.

Probability that the first draw is indigo:

P 1 = 15 85 = 3 17 P_1=\dfrac{15}{85}=\dfrac{3}{17}

Probability that the second draw is indigo:

P 2 = 14 84 P_2=\dfrac{14}{84}

The probability that both marbles are indigo is

P = 3 17 ( 14 84 ) = 1 34 P=\dfrac{3}{17}(\dfrac{14}{84})=\dfrac{1}{34}

Alternate solution:

Since the two draws are without replacement, the act is the same as drawing two marbles together. The number of ways of choosing 2 2 marbles from 15 15 indigo marbles is 15 C 2 15C2 or 105 105 ways. The number of ways of choosing 2 2 marbles from 85 85 marbles is 85 C 2 85C2 or 3570 3570 . Thus, the probability is

P = 105 3570 = 1 34 P=\dfrac{105}{3570}=\dfrac{1}{34}

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