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(B1) = P(drawing black ball from bag on first draw)

P(W1) = P(drawing white ball from bag on first draw)

P(B2) = P(drawing black ball from bag on second draw)

P(W2) = P(drawing white ball from bag on second draw)

We need to find:

P(SWB) = P(one ball is White and other is black)

P(SWB) = P(first drawn is White and next is black) + P(first drawn black and next is white)

P(SWB) = P(DWB) + P(DBW)

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

The required probability is .

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