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# Divide a line segment into two parts by selecting a point ISBN: 9780321923271 41

## Solution for problem 13E Chapter 1.1

Probability and Statistical Inference | 9th Edition

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Problem 13E

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.

Step-by-Step Solution:
Step 1 of 3

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) = + = ...

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321923271

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