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# Probability

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A bag contains 6 red marbles, 5 blue marbles and 8 green marbles. If three marblesare drawn out of the bag, what is the probability, to the nearest 10th of a percent, that all three marbles drawn will be green?

May 7, 2022

### 1+0 Answers

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Number of ways to pick out 3 green marbles = $$\binom{8}3$$

Number of ways to pick out 3 marbles = $$\binom{6 + 5 + 8}3 = \binom{19}3$$.

Probability = $$\dfrac{\binom83}{\binom{19}3} = \dfrac{56}{969}$$.

Now you can round that to the nearest 10th of a percent, which is just the nearest 0.001.

Interesting fact: The probability is quite close to $$\dfrac{1}{10\sqrt 3}$$.

May 8, 2022