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?
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 
.