A point M is randomly selected from a segment AB whose length is 9. What is the probability that the longest segment between AM and MB has the length no more then 6?

Question

A point M is randomly selected from a segment AB whose length is 9. What is the probability that the longest segment between AM and MB has the length no more then 6?

Answer 1

Think of the line segment AB as a subset of the number line where:

A: x=0

B: x=9

Since Point M is a randomly selected number from AB, then its relative distance from 0, say X will be uniformly distributed from 0 to 9.

Now, we want P( longer segment between AM and MB has length no more than 6)

= P( 3<X<6) [for the longer segment not to exceed a length of 6, it should fall between 3 and 6]

= (6-3)/(9-0) [using the Uniform distribution]

=1/3 QED