# An Urn Contains 9 Balls Two of Which Are Red, Three Blue and Four Black. Three Balls Are Drawn at Random. the Probability that They Are of the Same Colour is (A) 5/84 (B) 3/9 (C) 3/7 (D) 7/17 - Mathematics

MCQ

An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is

•  5/84

•  3/9

•  3/7

• 7/17

#### Solution

5/84

Three balls can be drawn randomly from nine balls in 9C3 = 84 ways.
Three balls cannot be red as there are only two red balls.
Three balls of the same colour can be drawn in the following ways :
3 blue out of a total of 3 blue balls.
The probability for which is $\frac{^{3}{}{C}_3}{84} = \frac{1}{84}$

3 black out of a total of 4 black balls.
The probability for which is $\frac{^{4}{}{C}_3}{84} = \frac{4}{84}$

Hence, required probability =$\frac{1}{84} + \frac{4}{84} = \frac{5}{84}$

Concept: Probability - Probability of 'Not', 'And' and 'Or' Events
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Q 27 | Page 72