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 p. 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?
Answer to relevant QuestionsSuppose that each child born to a couple is equally likely to be a boy or a girl, independently of the sex distribution of the other children in the family. For a couple having 5 children, compute the probabilities of the ...A and B play a series of games. Each game is independently won by A with probability p and by B with probability 1 − p. They stop when the total number of wins of one of the players is two greater than that of the other ...A person tried by a 3-judge panel is declared guilty if at least 2 judges cast votes of guilty. Suppose that when the defendant is in fact guilty, each judge will independently vote guilty with probability .7, whereas when ...As a simplified model for weather forecasting, suppose that the weather (either wet or dry) tomorrow will be the same as the weather today with probability p. Show that the weather is dry on January 1, then Pn, the ...(a) An urn contains n white and m black balls. The balls are withdrawn one at a time until only those of the same color are left. Show that, with probability n/(n + m), they are all white. Imagine that the experiment ...
Post your question