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A box contains 20 marbles, 8 red, 12 green. You draw three randomly. What is the probability that none of them are green.

User ReBa
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Final answer:

The probability of drawing three red marbles without any green marbles is 14/285.

Step-by-step explanation:

To find the probability that none of the marbles drawn are green, we need to calculate the probability of drawing a red marble on each of the three draws. The probability of drawing a red marble on the first draw is:

P(red on 1st draw) = number of red marbles / total number of marbles = 8/20 = 2/5

Since marbles are drawn without replacement, the probability of drawing a red marble on the second draw is:

P(red on 2nd draw) = number of remaining red marbles / remaining total number of marbles = 7/19

Similarly, the probability of drawing a red marble on the third draw is:

P(red on 3rd draw) = 6/18 = 1/3

To find the probability of all three events happening, we multiply the individual probabilities:

P(none of them are green) = P(red on 1st draw) x P(red on 2nd draw) x P(red on 3rd draw) = (2/5) x (7/19) x (1/3) = 14/285.

User Krackmoe
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