Answered: A general is planning to invade towns…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A general is planning to invade towns A, B, and C and has 20 soldiers at his disposal (6 officers and 14 privates). After some thought, the general decides to select 12 soldiers to carry out the invasion and to keep the remaining 8 (and himself) behind to protect the command post. a) If the general selects the 12 soldiers randomly, and without replacement, what is the probability that 3 will be officers and 9 will be privates? b) If the general now takes the 12 selected soldiers (3 officers and 9 privates) and randomly selects 4 soldiers (without replacement) to invade each of towns A, B, and C, what is the probability that exactly 1 officer ends up being sent to each town? 2. A project director runs a staff consisting of 6 scientists and 3 lab technicians. Three new projects have to be worked on and the director decides to assign 4 of her staff to the first project, 3 to the second, and 2 to the third. In how many ways can this be accomplished if: a) The director assigns her staff to the projects randomly? b) Each project requires 1 lab technician? c) Of the 4 people assigned to the first project, at least 3 are scientists? 3. Ten officers and 10 regular soldiers are going to be assigned to units of size 4, 6, and 10 to carry out different missions. If assignment is done at random, what is the probability that each unit will end up being half officers and half regular soldiers? 4. Each week, Bob and three friends from work pool their money together and buy 12 lottery tickets that are randomly and equally divided up among the group. a) How many ways can the tickets be divided up among Bob and his friends? b) By an incredible stroke of luck, this week there are two winning tickets among the 12 tickets purchased by Bob and his friends. What is the probability that different people end up with these winning tickets? c) In Lotto Mania, the game played by Bob and his friends, six winning numbers are selected by random sampling without replacement from a bin of balls numbered 1 through 30. A player wins if the six numbers on his/her ticket match at least five numbers from the six winning numbers (order is irrelevant). If you buy a single ticket, what is the probability that you will win something? 5. A sales company purchases 15 new cars for its top salespeople: 6 identical Chevrolets, 5 identical Fords, and 4 identical Toyotas. a) If 5 of these 15 cars are randomly assigned to the salespeople, what is the probability that none of them is a Ford? b) If 3 of the 15 cars are randomly assigned to the salespeople, what is the probability that at least 2 of them are Toyotas? c) If 3 of the 15 cars are randomly assigned to the salespeople, what is the probability that they are all a different model? d) If the company parking lot has 15 parking spaces in a row and the 15 new cars were parked at random, what is the probability that all the same-model cars would end up being parked next to each other? Answers: 1. a) b) .2909 2. a) b) 360 3. a) .164 4. a) b) .8182 .3179 1260 c) 750 369600 c) .0002442 5. a) b) .154 c) .264 d) .000009514

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