Q. 74.0( 5 Votes )

# A bag contains 3 white, 4 red and 5 black balls. Two balls are drawn one after the other, without replacement. What is the probability that one is white and the other is black?

Answer :

Given:

⇒ Bag contains 3 white, 4 red and 5 black balls.

It is told that two balls are drawn from bag without replacement.

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

⇒ P(B_{1}) = P(drawing black ball from bag on first draw)

⇒

⇒

⇒

⇒ P(W_{1}) = P(drawing white ball from bag on first draw)

⇒

⇒

⇒

⇒ P(B_{2}) = P(drawing black ball from bag on second draw)

⇒

⇒

⇒ P(W_{2}) = P(drawing white ball from bag on second draw)

⇒

⇒

We need to find:

⇒ P(S_{WB}) = P(one ball is White and other is black)

⇒ P(S_{WB}) = P(first drawn is White and next is black) + P(first drawn black and next is white)

⇒ P(S_{WB}) = P(D_{WB}) + P(D_{BW})

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

⇒

⇒

⇒

⇒

⇒

∴ The required probability is .

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