Question 1044326: If a randomly selected, non-negative single-digit integer is added to set X = {2,3,7,8}, what is the probability that the median of the set will increase while its range will remain the same ?
a)20%
b)30%
c)40%
d)50%
e)60%
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! Here are the new sets after a non-negative single-digit integer was added to X:
The median of X is 5 and its range is 6.
{ 0,2,3,7,8 } ===> median is 3, range is 8
{ 1,2,3,7,8 } ===> median is 3, range is 7
{ 2,2,3,7,8 } ===> median is 3, range is 6
{ 2,3,3,7,8 } ===> median is 3, range is 6
{ 2,3,4,7,8 } ===> median is 4, range is 6
{ 2,3,5,7,8 } ===> median is 5, range is 6
{ 2,3,6,7,8 } ===> median is 6, range is 6
{ 2,3,7,7,8 } ===> median is 7, range is 6
{ 2,3,7,8,8 } ===> median is 7, range is 6
{ 2,3,7,8,9 } ===> median is 7, range is 7,
that gives three instances where the median is greater than 5 and the range is still 6. Therefore the answer is 30%.
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