Three urns respectively contain 2 white and 3 black, 3 white and 2 black and 1 white and 4 black balls. If one ball is drawn from each urn, then the probability that the selection contains 1 black and 2 white balls is

Step-by-step solution

Solution: Let each urn contain 5 balls. The probability of drawing white from urn 1 is P(W₁)= 2 5 , black P(B₁)= 3 5 . For urn 2: P(W₂)= 3 5 , P(B₂)= 2 5 . For urn 3: P(W₃)= 1 5 , P(B₃)= 4 5 . The selection of one black and two white balls occurs in three mutually exclusive cases: Black from urn 1: 3 5 3 5 1 5 = 9 125 Black from urn 2: 2 5 2 5 1 5 = 4 125 Black from urn 3: 2 5 3 5 4 5 = 24 125 The total probability sums to 9 125 + 4 125 + 24 125 = 37 125 . 37 125