Suppose that n is a positive integer with n > 3. Three distinct integers are chosen from the set {1, 2, 3, ..., n – 1, n} and arranged from smallest to largest. (The set contains exactly the smallest n positive integers.) Determine the probability that the middle integer of these three is greater than or equal to the average of the largest and the smallest.

Suppose that n is a positive integer with n > 3. Three distinct integers are chosen from the set {1, 2, 3, ..., n – 1, n} and arranged from smallest to largest. (The set contains exactly the smallest n positive integers.) Determine the probability that the middle integer of these three is greater than or equal to the average of the largest and the smallest.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

Suppose that n is a positive integer with n > 3. Three distinct integers are chosen from the
set {1,2,3, ...,n – 1, n} and arranged from smallest to largest. (The set contains exactly the
smallest n positive integers.) Determine the probability that the middle integer of these three
is greater than or equal to the average of the largest and the smallest.
-

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