If a randomly selected non-negative single digit integer is added to {2, 3, 6, 8}. What is the probability that the median of the set will increase but the range still remains the same?
Choose the correct choice from the following answers:  A) 0.2  B) 0.3  C) 0.4  D) 0.5  E) 0.6

Rationale: "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 6 ) / 2 = 4.5 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c ."
Answer: C