Solutions
Step I: All balls from bag D transferred to bag E
Number of black balls in bag E =
Number of red balls in bag E =
Number of white balls in bag E =
Step II: Half of each colour of ball transferred to bag B from bag E
Number of black balls in bag E =
Number of red balls in bag E =
Number of white balls in bag E =
Now, total number of balls in bag E after transferring =
Required probability = (15C2 × 6C1 + 15C3)/21C3 = 31/38
So option (D) is the correct answer.