1. Coin Tossing We have a peculiarly biased coin for which the probability of tossing heads changes after each flip. Initially (on the first flip), the probability of heads is 1/2. But for each successive toss the probability decreases by a multiplicative factor of 1/4, so that on the ith flip the probability of heads is 1/2 x (1/4)1-1. We toss the coin n times (a) What is the probability that all n tosses were heads? (b) In general, what is the expected number of heads we will get