Refer to the Chance (Fall 2007) study on making your vote count, Exercise 3.29. Recall the scenario where you are one of five county commissioners voting on an issue, and each commissioner is equally likely to vote for or against.

a. Your vote counts (i.e., is the decisive vote) only if the other four voters split, two in favor and two against.

Use the binomial distribution to find the probability that your vote counts.

b. If you convince two other commissioners to "vote in bloc" (i.e., you all agree to vote among yourselves first, and whatever the majority decides is the way all three will vote, guaranteeing that the issue is decided by the bloc), your vote counts only if these two commissioners split their bloc votes, one in favor and one against. Again, use the binomial distribution to find the probability that your vote counts.