Please help me with that problem, IT IS JUST ONE PROBLEM.... PLEASE DO IT STEP BY STEP... AND DON'T COPY THE ANSWER FROM ANOTHER NETWORLD.

3.75. 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 legislation. 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 . What is the probability that a given steering committee member'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? What is the corresponding probability for a given council member not on the steering committee?

THE PHOTO HAS THE REAL PROBLEM

1. Do Chapter 3, Problem 75, but considering only the case p : 1/2. Answer only the rst question: What is the probability that a given steering committee member's vote is decisive in the sense that if that person's vote were reversed, then the nal fate of the legislation would be reversed? (Note: There are some answers on the web for this book problem which are incorrect.) To set up the problem: note there are 7 voters. Set up voters 1-3 on the steering committee, and voters 47 as not on the steering committee. Focus on voter 1. Thus there are 27 : 128 possible outcomes. A key question obviously is: For how many of these 128 outcomes is voter 1's vote decisive? To make sure you understand the problem, it's best to answer this question for a few example outcomes, before you start setting up the computation. Would your answer be different if you consider voter 2