Non-negative single digit integer varies from 0 to 9 (10 nos)

Condition is Median must increase and range should remain the same.

Existing Set is (2,3,7,8). When you add nos 0 to 9 to the set, only 3 nos satisfy the conditions --> 6,7,8.

So, probability is 3/10 or 30%.

For the range to stay the same the number chosen must be 2, 3, 4, 5, 6, 7, 8 - for the median to increase you need numbers larger than the current median - the current median is 5 -- (3+7)/2 Thus only the numbers 6, 7 or 8 will suffice.

For probability you need want over total - there are three numbers that will satisfy what you want and 10 total numbers therefore the answer is B - 30%