A box contains 4 coins. Coin 1 is biased such that it comes up heads with probability 0.3. Coin 2 is fair, and equally likely to come up heads or tails. Coin 3 is biased such that it comes up heads with probability 0.75. Finally, coin 4 has heads on both sides of the coin. Let's define the following events: Let Ci = "coin i is selected" (i = 1, 2, 3, 4). Let Hj = "the jth toss comes up heads", j=1,..,5. When answering the questions below, express your solution in terms of the events defined above. a. A coin is randomly selected from the box and is tossed. What is the probability that this first toss comes up heads? Number b. If the first toss comes up heads, what is the probability that coin I was tossed? Number c. If the same coin is tossed a second time, and another head is obtained, what is the probability that coin I was tossed? Number d. Now consider a sequence of 5 tosses of the same coin. Suppose that we observe the sequence: HHHTT. What is the probability that we tossed coin 1? Number