7. You are on an island inhabited by three types of people: those who only tell the truth (knights),those who only tell lies (knaves), and those who sometimes tell the truth and sometimes tell lies(spies). Knaves are said to be of the lowest rank, spies of middle rank, and knights of highestrank. Two people stand before you: A and B.A says, "I am a knave and you are a spy."B says, "That is not true. I am of lower rank than you."What are A and B?●A is a knight, B is a knightA is a knight, B is a spy

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Answered: 7. You are on an island inhabited by…

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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Suppose that there are five young women and six young men on an island. Each woman is willing to marry some of the men on the island and each man is willing to marry any woman who is willing to marry him. Suppose that Anna is willing to marry Jason, Larry, and Matt; Barbara is willing to marry Kevin and Larry; Carol is willing to marry Jason, Nick, and Oscar; Diane is willing to marry Jason, Larry, Nick, and Oscar; and Elizabeth is willing to marry Jason and Matt. Identify the correct statements with respect to the matching between men and women formed in the previous question. (Check all that apply.) Check All That Apply It is a complete matching from the set of women to the set of men. It is not a complete matching from the set of women to the set of men. It is a maximum matching, since complete matching is always a maximum matching. × × It is not a maximum matching, because complete matching need not be always a maximum matching. ×
Consider the following problem: Three officers-a president, a treasurer, and a secretary-are to be chosen from among four people: Ann, Bob, Cyd, and Dan. Suppose that, for various reasons, Ann cannot be president and either Cyd or Dan must be secretary. How many ways can the officers be chosen?
In a game show, a contestant is presented with three doors: Door A, Door B, and Door C. Behind one of these doors is a car, and behind the other two are goats. The contestant picks one door, say Door A, and the host, who knows what's behind each door, opens another door, say Door B, revealing a goat. The contestant is then given the choice to stick with their original choice (Door A) or switch to the remaining unopened door (Door C). What is the probability of winning the car if the contestant decides to switch doors?
In a survey of 252 professional athletes, it was found that 119 of them owned a convertible, 122 of them owned a giant screen TV, and 115 owned a sporting goods store. 21 owned a convertible and a store, 44 owned a TV and a store, and 73 owned a covertible and a TV. 13 owned all three items. How many athletes did not own any of the three items? How many owned a covertible and a TV, but not a store? How many athletes owned a convertible or a TV? How many athletes owned exactly one type of item in the survey? How many athletes owned at least one type of item in the survey? How many owned a TV or a store, but not a convertible?
A company is organizing a team-building event with various activities. There are 12 employees attending the event, and they need to be split into three teams: Team A, Team B, and Team C. Each team should have at least 2 members but no more than 6 members. In how many different ways can the teams be formed? (Note: The order of the teams doesn't matter; i.e., Team A, Team B, and Team C is the same as Team C, Team A, and Team B.)
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There are 40 men in class. 29 of them have no facial hair (i.e. neither a beard nor a mustache). If 7 of the men have beards and 9 of the men have mustaches, how many of the men in the class have both a beard and a mustache? O A. 2 В. 4 O c. 5 D. 7 ОЕ. 16

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