If 3 marbles are drawn at random, what is the probability that none is red ?

Solution

Number of ways of drawing 3 marbles out of 16

$$n(S) = C^{16}_3 = \frac{16 \times 15 \times 14}{1 \times 2 \times 3}$$

= $$560$$

Out of the three drawn marbles, none is red, i.e., they will be either blue or green.

=> $$n(E) = C^8_3 = \frac{8 \times 7 \times 6}{1 \times 2 \times 3}$$

= $$56$$

$$\therefore$$ Required probability = $$\frac{n(E)}{n(S)}$$

= $$\frac{56}{560} = \frac{1}{10}$$

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