Suppose Ethernet physical addresses are chosen at random using true random bits). (a) What is the probability that on a 1024-host network, two addresses will be the same? (b) What is the probability that the above event will occur on o or more of 220 networks? (c) What is the probability that, of the 230 hosts in all the networks of (b), some pair has the same address? Hint: The calculation for (a) and (c) is a variant of that used in solving the so-called Birthday Problem: Given N people, what is the probability that two of their birthdays (addresses) will be the same? The second person has probability 1-3 of having a 365 different birthday from the first, the third has probability 1 of having a different birthday from the first two, and so on. The probability that all birthdays are different is thus - (1-325)×(1-325)××(1-N5¹) which for smallish N is about 1- 1+2++ (N-1) 365 2 365

Suppose Ethernet physical addresses are chosen at random using true random bits). (a) What is the probability that on a 1024-host network, two addresses will be the same? (b) What is the probability that the above event will occur on o or more of 220 networks? (c) What is the probability that, of the 230 hosts in all the networks of (b), some pair has the same address? Hint: The calculation for (a) and (c) is a variant of that used in solving the so-called Birthday Problem: Given N people, what is the probability that two of their birthdays (addresses) will be the same? The second person has probability 1-3 of having a 365 different birthday from the first, the third has probability 1 of having a different birthday from the first two, and so on. The probability that all birthdays are different is thus - (1-325)×(1-325)××(1-N5¹) which for smallish N is about 1- 1+2++ (N-1) 365 2 365

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Network transmission cabling

A network is a collection of devices connected by communication links. A device can be a computer or any instrument capable of sending and receiving data or information formed by other nodes toward the network. A channel that connects people or things is known as a network. It sends the data from one place to another. It is the basic concept of a computer, network, and data communications.

Question

Suppose Ethernet physical addresses are chosen at random
(using true random bits).
(a) What is the probability that on a 1024-host network, two
addresses will be the same?
(b) What is the probability that the above event will occur on one
or more of 220 networks?
(c) What is the probability that, of the 230 hosts in all the
networks of (b), some pair has the same address?
Hint: The calculation for (a) and (c) is a variant of that used in
solving the so-called Birthday Problem: Given N people, what is
the probability that two of their birthdays (addresses) will be the
same? The second person has probability 1-3 of having a
365
different birthday from the first, the third has probability 1 365
of having a different birthday from the first two, and so on. The
probability that all birthdays are different is thus
2
(1-365)×(1-325) × × (1-N5¹)
X X
365
which for smallish N is about
1+2+
1
· + (N − 1)
365
...

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