Answer :

Given:

⇒ Urn A contains 4 red balls and 3 black balls

⇒ Urn B contains 5 red balls and 4 black balls

⇒ Urn C contains 4 red balls and 4 black balls

It is told that one ball is drawn is drawn from is each urn.

We need to find the probability that two balls are red and other ball is black.

Let us find the Probability of drawing each colour ball from the Urn.

⇒ P(B_{1}) = P(drawing black ball from Urn A)

⇒

⇒

⇒

⇒ P(R_{1}) = P(drawing Red ball from urn A)

⇒

⇒

⇒

⇒ P(B_{2}) = P(drawing black ball from Urn B)

⇒

⇒

⇒

⇒ P(R_{2}) = P(drawing Red ball from urn B)

⇒

⇒

⇒

⇒ P(B_{3}) = P(drawing black ball from Urn C)

⇒

⇒

⇒

⇒ P(R_{3}) = P(drawing Red ball from urn C)

⇒

⇒

⇒

We need to find the probability of 2 red balls and 1 black ball from three bags

⇒ P(S) = P(drawing two red ball and one Black ball)

⇒ P(S) = P(drawing black balls from bag A red ball from bag B and Red ball from bag C) + P(drawing black balls from bag B red ball from bag A and Red ball from bag C) + P(drawing black balls from bag C red ball from bag A and Red ball from bag B)

Since drawing a ball is independent for each bag, the probabilities multiply each other.

⇒

⇒

⇒

⇒

⇒ .

∴ The required probability is .

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