An integer k ∈ {1,2,…,999,1000} is selected at random. What is the probability that: 1) k is divisible by 3? 2) k is divisible by 5 but not by 3? 3) k is a prime number or a composite number with a prime factor p ≤ 29?

An integer k ∈ {1,2,…,999,1000} is selected at random. What is the probability that: 1) k is divisible by 3? 2) k is divisible by 5 but not by 3? 3) k is a prime number or a composite number with a prime factor p ≤ 29?

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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Question

An integer k ∈ {1,2,…,999,1000} is selected at random. What is the probability that:

1) k is divisible by 3?
2) k is divisible by 5 but not by 3?
3) k is a prime number or a composite number with a prime factor p ≤ 29?

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Expert Solution

Step 1

It is given that $k$ is an integer selected at random from the set of numbers $\{1, 2, \dots, 999, 1000\}$ .

A prime number is a number that is divisible by 1 and itself only.

A composite number is a number that has more than 2 factors.

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