Answer:
On a Number Line, if only whole numbers are marked
Points J, M, K, and L are marked, having coordinates 0, 25, 5, and 12.
Two points are again marked on the number line.
Probability,that a point on J M is placed first on J L
= There are 10 natural numbers in between J L and 12 natural numbers between L M.
So, Required Probability
[tex]=\frac{_{1}^{C}\textrm{10}\times_{1}^{C}\textrm{12}}{_{1}^{C}\textrm{25}\times_{1}^{C}\textrm{25}}\\\\=\frac{10*12}{25*25}\\\\=\frac{120}{625}\\\\=\frac{24}{125}[/tex]
Now, Probability that second point is not placed on KL, it means that point is either is on J K or L M.
There are 4 natural number between 0 and 5 and 12 natural number between L and M.
Probability of marking second point on J M is
[tex]=\frac{_{1}^{C}\textrm{4}\times_{1}^{C}\textrm{12}}{_{1}^{C}\textrm{25}\times_{1}^{C}\textrm{25}}\\\\=\frac{4*12}{25*25}\\\\=\frac{48}{625}[/tex]
Probability of marking two points on the number line, with given condition is
[tex]=\frac{120}{625}+\frac{48}{625}\\\\=\frac{168}{625}[/tex]
If you consider ,points on the number line which are real numbers, then we can't find the required Probability that is marking two points on the line segment.
