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Chapter 6: Q.6.17 (page 279)

Three points X1,X2,X3 are selected at random on a line L. What is the probability thatX2 lies between X1andX3?

Short Answer

Expert verified

The probability that X2lies between X1andX3is13

Step by step solution

01

To find

The probability thatX2lies between X1andX3

02

Explanation

Three points to consider On a line L,X1,X2,X3are chosen at random.

The number of ways to arrange n items all at once=n!.

Total number of point=3As a result, the number of ways to arrange three points on a line is=3!=6

The possible arrangements are:

X1X2X3X1X3X2X2X1X3X2X3X1X3X1X2X3X2X1

Out of these X2liesbetweenX1andX3in2arrangements

Therefore X2liesbetweenX1andX3=26=13

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Most popular questions from this chapter

The random vector (X, Y) is said to be uniformly distributed over a region R in the plane if, for some constant c, its joint density is f(x, y) =  c if(x, y) 鈭� R 0 otherwise

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