Suppose that if a presidential election were held today, 53% of all voters would vote for candidate Smith over candidate Jones. (You can substitute the names of the most recent presidential candidates.) This problem shows that even if there are 100 million voters, a sample of several thousand is enough to determine the outcome, even in a fairly close election.

a. If 1500 voters are sampled randomly, what is the probability that the sample will indicate (correctly) that Smith is preferred to Jones?

b. If 6000 voters are sampled randomly, what is the probability that the sample will indicate (correctly) that Smith is preferred to Jones?