A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning heads on the first toss, followed by two tails). The 8 outcomes are listed below. Assume that each outcome has the same probability. Complete the following. Write your answers as fractions. (If necessary, consult a list of formulas.) (a) Check the outcomes for each of the three events below. Then, enter the probability of each event. Outcomes Probability HHHHHT HTH HTT THH THT| TTH TTT Event A: The first toss is heads Event B: More heads than tails Event A and B: The first toss is heads and more heads than tails (b) Suppose the first toss is heads. (That is, Event A occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event B. Then, enter the probability that Event B occurs given that Event A occurs. Outcomes given the first toss is heads Probability HHH HHT HTHHTT ? Event B: More heads than tails (c) Give the following probabilities and select the correct option below. P(A and B) P(A) P(B|A) P(A and B) P(A) P(B|A) %3D