Instructions

Answer the following questions based on the information given below.
A bowl contains 4 red, 3 green, 2 blue and 5 black marbles.

Question 128

If three marbles are drawn at random, what is the probability that none of them are black ?

Solution

The total number of marbles present is $$5+4+3+2 = 14$$
The number of ways of picking three marbles from them is $$^{14}C_3 = 364$$

If no marble is black, the three marbles should be picked from $$4+3+2 = 9$$ marbles.
The number of ways in which this can be done is $$^9C_3 = 84$$

Hence, the required probability is $$\frac{84}{364} = \frac{21}{91} = \frac{3}{13}$$

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