(a) Use the technique shown in Example 9.1.4 to find the number of positive three-digit integers that are multiples of 6. The smallest positive three-digit integer that is a multiple of 6 is 6 - The largest positive three-digit integer that is a multiple of 6 is 6. Therefore, the number of three-digit integers that are multiples of 6 is (b) What is the probability that a randomly chosen positive three-digit integer is a multiple of 6? (c) What is the probability that a randomly chosen positive three-digit integer is a multiple of 7?
(a) Use the technique shown in Example 9.1.4 to find the number of positive three-digit integers that are multiples of 6. The smallest positive three-digit integer that is a multiple of 6 is 6 - The largest positive three-digit integer that is a multiple of 6 is 6. Therefore, the number of three-digit integers that are multiples of 6 is (b) What is the probability that a randomly chosen positive three-digit integer is a multiple of 6? (c) What is the probability that a randomly chosen positive three-digit integer is a multiple of 7?
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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Please help me with this I’m confused, please show the step how u get the answer so I can understand it. Thanks!

Transcribed Image Text:(a) Use the technique shown in Example 9.1.4 to find the number of positive three-digit integers that are multiples of 6.
The smallest positive three-digit integer that is a multiple of 6 is 6 ·
The largest positive three-digit integer that is a multiple of 6 is 6 ·
Therefore, the number of three-digit integers that are multiples of 6 is
(b) What is the probability that a randomly chosen positive three-digit integer is a multiple of 6?
(c) What is the probability that a randomly chosen positive three-digit integer is a multiple of 7?

Transcribed Image Text:Example 9.1.4
Counting the Elements of a Sublist
a. How many three-digit integers (integers from 100 to 999 inclusive) are divisible by 5?
b. What is the probability that a randomly chosen three-digit integer is divisible by 5?
Solution
a. Imagine writing the three-digit integers in a row, noting those that are multiples of 5
and drawing arrows between each such integer and its corresponding multiple of 5.
100 101 102 103 104 105
106
107 108 109 110
994 995 996 997
998 999
5-20
5-21
5.22
5.199
From the sketch it is clear that there are as many three-digit integers that are mul-
tiples of 5 as there are integers from 20 to 199 inclusive. By Theorem 9.1.1, there are
199 - 20+ 1, or 180, such integers. Hence there are 180 three-digit integers that are
divisible by 5.
and
b. By Theorem 9.1.1 the total number of integers from 100 through 999 is 999 – 100+1 =
900. By part (a), 180 of these are divisible by 5. Hence the probability that a randomly
chosen three-digit integer is divisible by 5 is 180/900 = 1/5.
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