Does your vote matter? Consider a common situation in which a vote takes place among a group of people and the winning result is associated with having one vote greater than the losing result. For example, if a management board of 11 members votes Yes or No on a particular issue, then minimally a 6-to-5 vote is needed to decide the issue either way. Your vote would have mattered if the other members voted 5-to-5.

(a) You are on this committee of 11 members. Assume that there is a 50% chance that each of the other members will vote Yes, and assume that the members are voting independently of each other. What is the probability that your vote will matter?

(b) There is a closely contested election between two candidates for your town mayor in a town of 523 eligible voters. Assume that all eligible voters will vote with a 50%

chance that a voter will vote for a particular candidate.

What is the probability that your vote will matter?