1. Suppose a fair coin is tossed n times. Find the probability that exactly half of the tosses result in heads when n D 10; 30; 50. Where does the probability seem to converge as n becomes large?
2. Suppose one coin with probability .4 for heads, one with probability .6 for heads, and one that is a fair coin are each tossed once. Find the pmf of the total number of heads obtained. Is it a binomial distribution?
3. Suppose the IRS audits 5% of those having an annual income exceed- ing 200,000 dollars. What is the probability that at least one in a group of 15 such individuals will be audited? What is the expected number that will be audited? What is the most likely number of people who will be audited?
4. Suppose that each day the price of a stock moves up 12.5 cents with probability 1/3 and moves down 12.5 cents with probability 2/3. If the movements of the stock from one day to another are independent, what is the probability that after ten days the stock has its original price?