Q. 275.0( 1 Vote )

# 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

Answer :

Balls in urn = 9

3 balls can be drawn in ^{9}C_{3} ways.

To draw the balls of same colour, we can select balls all three red, all blue or all black.

P(ball of same colour) = P(all blue) or P(all black) or P(all red)

P(all red) = not possible as we have to select 3 balls but there are only 2 red balls.

∴ P(All red) = 0

P(all black) =

And P(all blue) =

∴ P(ball of same colour) = P(all blue) or P(all black) or P(all red)

⇒ P(ball of same colour) = P(all blue) + P(all black) + P(all red)

= 1/84 + 1/21 + 0 = 5/84

Our answer matches with option (a)

∴ Option (a) is the only correct choice

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