Probability

Concept:Use law of total probability based on the colour of the transferred ball.Explanation:First urn: 3 red, 5 white (total 8). Second urn initially: 4 red, 6 white (total 10).Case 1: Transferred ball is red. Probability = $\frac{3}{8}$.Then second urn has 5 red, 6 white (total 11). Probability second ball is red = $\frac{5}{11}$.Contribution: $\frac{3}{8} \times \frac{5}{11} = \frac{15}{88}$.Case 2: Transferred ball is white. Probability = $\frac{5}{8}$.Then second urn has 4 red, 7 white (total 11). Probability second ball is red = $\frac{4}{11}$.Contribution: $\frac{5}{8} \times \frac{4}{11} = \frac{20}{88}$.Total probability = $\frac{15}{88} + \frac{20}{88} = \frac{35}{88}$.Answer:$\frac{35}{88}$