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Complementary Event

A box contain...

Question

A box contains 2 red, 3 black and 5 white balls. If 3 balls are drawn at a random without replacement, find the probabilities that
a) all 3 are black
b) 2 are red and 1 black
c) at least 1 is white

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Solution

There are totally 10 balls - 2R + 3B + 5 W
Hence, the total number of possible combinations when 3 balls are drawn out of 10 balls = 10 C 3
There are 3 B balls. Hence, the total number of possibilities of getting 3 B out of 3 balls = 3 c 3 = 1
Hence, the required probability $= \frac{1}{(10 C 3)} = \frac{1}{120}$

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