Box 1 contains balls numbered 1 , 2 , and 3 in the ratio 1:2:3 . Box 2 contains balls numbered 0 , 1 , and 2 in the ratio 3:2:1 . One ball is drawn at random from each box independently. The probability that the absolute difference between the numbers on the drawn balls is exactly 1 is

Step-by-step solution

Let X be the number on the ball drawn from Box 1 and Y be the number on the ball drawn from Box 2. The probability distribution for Box 1 is: P(X=1) = 1 6 , P(X=2) = 2 6 , P(X=3) = 3 6 The probability distribution for Box 2 is: P(Y=0) = 3 6 , P(Y=1) = 2 6 , P(Y=2) = 1 6 We need to find the probability of the event |X - Y| = 1 . The favorable ordered pairs (X, Y) are (1, 0) , (1, 2) , (2, 1) , and (3, 2) . Calculating the probability for each pair: P(X=1, Y=0) = 1 6 3 6 = 3 36 P(X=1, Y=2) = 1 6 1 6 = 1 36 P(X=2, Y=1