The probability that it is closer to the point 4 than to either end is:
[tex]\dfrac{1}{2}[/tex]
If we divide the number line between 2 to 8 into 6 equal parts i.e. 2-3-4-5-6-7-8
Then the number is closer to the point 4 than to the either end if it will lie in the part:
3-4-5-6
( Because if it will lie between 2-3 then it will be close to 2 and not to 4.
If it will lie between 6-7 or 7-8 then it will be close to 8 and not close to 4)
Hence, the number of parts the number may lie such that it is close to 4 is: 3
and the total number of parts are: 6
Hence, the probability that the number is close to 4 than to either end is the ratio of the number of parts where it is close to 4 to the total number of parts.
i.e.
The probability is:
[tex]Probability=\dfrac{3}{6}\\\\i.e.\\\\Probability=\dfrac{1}{2}[/tex]
