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Divide a line segment into two parts by selecting a point
Chapter 1, Problem 13E(choose chapter or problem)
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.
Questions & Answers
QUESTION:
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:
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})