If a randomly selected non-negative single digit integer is added to {2, 3, 4, 7}. 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 choices.
A) 0.2 B) 0.3 C) 0.4 D) 0.5 E) 0.6
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 + 4)/2= 
<gadget id="calculator"> (3 + 4)/2</gadget>
<output>7/2 = around 3.5</output>
3.5, thus the number selected must be 4 or greater.   For the range to remain the same, the number must be between 2 and 7 inclusive.   To satisfy both conditions, the number selected must be 4, 5, 6, or 7.   The probability is  4/10= 
<gadget id="calculator"> 4/10</gadget>
<output>2/5 = around 0.4</output>
0.4   The answer is 0.4.
<result>C</result>
If a randomly selected non-negative single digit integer is added to {2, 3, 4, 7}. What is the probability that the median of the set will increase but the range still remains the same?