A town council of 7 members contains a steering committee of size 3. New ideas for legislation go first to the steering committee and then on to the council as a whole if at least 2 of the 3 committee members approve the leg- islation. Once at the full council, the legislation requires a majority vote (of at least 4) to pass. Consider a new piece of legislation, and suppose that each town council member will approve it, independently, with probability p=1/2. What is the probability that a given steering committee mem- ber’s vote is decisive in the sense that if that person’s vote were reversed, then the final fate of the legislation would be reversed?

A town council of 7 members contains a steering committee of size 3. New ideas for legislation go first to the steering committee and then on to the council as a whole if at least 2 of the 3 committee members approve the leg- islation. Once at the full council, the legislation requires a majority vote (of at least 4) to pass. Consider a new piece of legislation, and suppose that each town council member will approve it, independently, with probability p=1/2. What is the probability that a given steering committee mem- ber’s vote is decisive in the sense that if that person’s vote were reversed, then the final fate of the legislation would be reversed?

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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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

A town council of 7 members contains a steering
committee of size 3. New ideas for legislation go first to the
steering committee and then on to the council as a whole

if at least 2 of the 3 committee members approve the leg-
islation. Once at the full council, the legislation requires a

majority vote (of at least 4) to pass. Consider a new piece
of legislation, and suppose that each town council member
will approve it, independently, with probability p=1/2. What

is the probability that a given steering committee mem-
ber’s vote is decisive in the sense that if that person’s vote

were reversed, then the final fate of the legislation would
be reversed?

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