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Chapter 6: Q6.17 (page 272)

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

Short Answer

Expert verified

The probability that X2 lies between X1 and X3 is13

Step by step solution

01

Content Introduction 

Three points X1 , X2 , X3 are selected at a random on a line L.

Number of ways of arranging and things taking all at a time is n!. Total number of points is 3.

So, the number of ways of arranging 3 points on a line is 3! which is equal to 6.

02

Content Explanation

Possible arrangements are:

X1X2X3X1X3X2X2X1X3X2X3X1X3X1X2X3X1X2

Out of these X2 lies between X1 and X3in two arrangements.

Therefore, Probability that X2lies between X1and X3is=26=13

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Most popular questions from this chapter

A model proposed for NBA basketball supposes that when two teams with roughly the same record play each other, the number of points scored in a quarter by the home team minus the number scored by the visiting team is approximately a normal random variable with mean 1.5 and variance 6. In addition, the model supposes that the point differentials for the four quarters are independent. Assume that this model is correct.

(a) What is the probability that the home team wins?

(b) What is the conditional probability that the home team wins, given that it is behind by 5 points at halftime?

(c) What is the conditional probability that the home team wins, given that it is ahead by 5 points at the end of the first quarter?

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(a) Find the probability that exactly 3of the next 6months have sales greater than 100.

(b) Find the probability that the total of the sales in the next 4months is greater than 420.

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