PROBLEM 13E

Divide a line segment into two parts by selecting a point at random. Use your intuition to assign a probability to the event that the longer segment is at least two times longer than the shorter segment.

Answer:

Step1 of 1:

Consider the line as part of number line from 0 to 1, choosing a point same as choosing a line. So f(x) = 1.

Let choose point ‘A’ corresponding to number ‘x’.

The required cases is

If x > 0.5 , = P({x: x > 2(1-x)})

If x < 0.5, = P({x: (1-x) < 2 x})

Then,

= P({x: x > and x < 1})

= P({x: x < and x >0})

Here, p(required) =+

=

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