12 21. A committee of four has to be formed from among 3 ceonomists, 4 engineersstatišticians and 1 doctor.(i) What is the probability that each of the four professions is represented on the committee?(ii) What is the probability that the omm consists of the doctor and at least one economist

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Answered: 9 12-21. A committee of four has to be…

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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9. One box contains six red balls and four green balls, and a second box contains seven red balls and three green balls. A ball is randomly chosen from the first box and placed in the second. Then a ball is randomly selected from the second box and placed in the first box. (a) What is the probability that a red ball is selected from the first box and a red ball is selected from the second box? (b) At the conclusion of the selection process, what is the probability that the mmbers of red and green balls in the first box are identical to the numbers at the beginning? 10. One in every 100 people are infected by a virus. A test is used to determine whet her a person is infected. If a person is infected, the test is positive 70% of the time, but if the person is not infected, the test is still positive 10% of the time. (a) If a person tests positive, what is the probability that the person is infected? (b) If a person tests negative, what is the proba bility that the person is not infected?
36 employees work in a company X. For a special purpose, the Chairperson of that company chose 8 employees’ names and kept his selection secret. The Deputy Director and the General Manager also chose 4 and 5 employees respectively without letting each other know about their selections. (There might be common employees within DD’s choices and GM’s choices ). What is the probability that exactly 1 of DD’s chosen employees and 2 of GM’s chosen employees match the list of the Chairperson?
Bangladesh has 57 rivers. Turjo chooses 10 river names not letting Zawad know. After that Zawad chooses 5 Bangladeshi river names secretly again from those 57. What is the probability that at most 3 of Zawad’s selected rivers match Turjo’s choices?
1. Students can belong to one or more of three clubs, call them A,B, and C. The probability that a student belongs to either club A or B, but not C, is P((AUB)NC^) 40%. Moreover, the probability that a student belongs to either club A or B, and club C is 15%. Lastly, the probability that a student belongs only to club C, and neither A or B, is 20%. Find the probability that a student does not belong to any club.
A project group of 9 people will be formed among the engineers working in an enterprise. There are 10 mechanical, 6 electrical and 4 industrial engineers working in the enterprise. What is the probability that there will be 4 machines, 3 electrical and 2 industrial engineers in the project group. Solutions will be made using probability distribution functions 2

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