1. If you were to toss a fair coin eight times, among the sequences below, which one(s) do you think would be most likely (i.e. having the largest probability) to occur?
(i) HHHHHHHH, (ii) HHTHTHHT, (iii) HHHHTTTT, (iv) HTTHTHHT
(H denotes tossing a head; T denotes tossing a tail)
2. Suppose an insurance company charges $800 per year for a certain health insurance policy with a maximum payout of $20,000 when customer makes a claim. Each year, 3% of the customers submit a claim.
What is the average gain of the insurance company per customer who buys this policy?