> Example 2. A three-digit number (that is, a number from 100–999) is selected "at ran-dom." (“At random" means that we assume all numbers to have the same proba-bility of being selected.) What is the probability that all three digits are the same?There are 900 three-digit numbers; 9 of them (namely 111, 222, · ..all three digits the same. Hence the desired probability is m' , 999) have100

Answered: Example 2. A three-digit number (that…

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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A box contains N coins, m of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is 1/2, while it is 2/3 when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. What is the probability that the coin drawn is fair?
3) In a recent semester at a local university, 530 students enrolled in both General Chemistry and Calculus I. Of these students, 53 received an A in general chemistry, 83 received an A in calculus, and 25 received an A in both general chemistry and calculus. Find the probability that a randomly chosen student received an A in general chemistry or calculus.
One of the n encrypted files in a folder is a special file. K of these files are removed one at a time by an attacker who has access to the folder. Each choice has an equal chance of being any of the currently available files. What is the probability that the person will withdraw the special file?You must justify or explain how you arrived at your conclusion.
Three distinct numbers between 10 and 25 (inclusive) are chosen at random. What is the probability that the numbers are all composite numbers?
Suppose that the New England Colonials baseball team is equally likely to win a game as not to win it. If 4 Colonials games are chosen at random, what is the probability that exactly 3 of those games are won by the Colonials?
1) A particular gadget contains 50 integrated circuits (ICs). The probability that any one of these ICs is defective is 0.02. The gadget will function only if there is no defective IC. What is the probability that the gadget will function?
Twenty subjects volunteer for a study of a new cold medicine. Eight of the volunteers are ages 20-39, 6 are ages 40-59, and 6 are age 60 or older. If 8 volunteers are selected at random, find the following probabilities. a) the probability that all the volunteers selected are ages 20-39 b) the probability that 4 of the volunteers are ages 20-39 and 4 are age 60 or older. c) the probability that 4 of the volunteers are ages 40-59
There are twelve different chips in a bag: 6 red, 2 yellow and 4 blue. If two chips are drawn with replacement from the bag (one after the other), what is the probability that at least one of them is yellow? (Start with the appropriate formula in context.)
4. Teddy lives life on the edge and gets dressed randomly every morning. This morning, he is randomly choosing a pair of shoes, a pair of pants, and a shirt from his closet which contains the following colors and corresponding quantities: Shoes: black (2) and brown (3) Pants: black (3) and brown (1) Shirt: white (2), brown (4) and black (6) What is the probability that Teddy randomly chooses shoes, pants and a shirt of the same color? A. 1/5 В. 2/5 С. 120 A B C D D. 3/20
In a group of 36 university students, there are nine who are fluent in English, four in French and two in both languages (already counted among the above), if a student is selected at random and is known to be fluent in English. What is the probability that he is fluent in French?

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