In a box there are 8 red, 7 blue, and 6 white marbles. If 3 marbles are selected at random and the colors are noted, find the probability that all are red given that all are the same color.

Answer 1

The probability of getting a red on the first draw is 8/21. Since one red is gone and one marble is gone from the total, on the 2nd draw, the probability of getting red is 7/20. The probability of getting red on the 3rd draw is 6/19. So the probability of getting 3 reds is 8/21 • 7/20 • 6/19 = 336/7980.

The probability of getting a blue on the first draw is 7/21. The probability of getting blue on the 2nd draw is 6/20. The probability of getting blue on the 3rd draw is 5/19. So the probability of getting 3 blues is 7/21 • 6/20 • 5/19 = 210/7980.

The probability of getting a white on the first draw is 6/21. The probability of getting white on the 2nd draw is 5/20. The probability of getting white on the 3rd draw is 4/19. So the probability of getting 3 whites is 6/21 • 5/20 • 4/19 = 120/7980.

So given that all 3 colors match there are 336 + 210 + 120 or 666 possibilities. Out of those, 336 are red. So the probability is 336/666 = 56/111.

I think.

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