Suppose you are confronted with 2 coins, A and B. You are to make n tosses, using the coin you prefer at each toss. You will be paid 1 dollar for each time the coin falls heads. Coin A has probability t of falling heads, and coin B has probability I of falling heads. Unfortunately, you are not told which of the coins is coin A. Consequently, you decide to toss the coins according to the following system. For the first toss you choose a coin at random. For all succeeding tosses you select the coin used on the preceding toss if it fell heads, and otherwise switch coins. What is the probability that coin A will be the coin tossed on the nth toss if (i) n = 2, (ii) n = 4, (iii) n = 6, (iv) n is very large? What is the probability that the coin tossed on the nth toss will fall heads if (i) n = 2, (ii) n = 4, (iii) n = 6, (iv) n is very large?