We have to identify all the possible outcomes for each event described.
The event A is "A head on each of the first two tosses".
This means that the outcome will start with 2 H. The remaining letter, as we have only 3 tosses, can be H or T.
Then, the possible outcomes that correspond to this event are HHH and HHT.
The event B is "More heads than tails". This should include all the outcomes where the tails are no more than 1, as if we have an outcome with 2 or 3 tails, this would mean that there are more tails than heads.
Then, we can list the outcomes with no tails as HHH and the outcomes with only one tail as THH, HTH and HHT, as the tail can appear in any of the three tosses.
Then, the outcomes for this event are: HHH, THH, HTH and HHT.
The event C is "A tail on both the first and last tosses".
The outcomes that correspond to this event start and end with a T. We have two options for the second toss and it is T or H.
Then, the outcomes for this event will be TTT and THT.
As each outcome has the same probability (we have a fair coin) and we have 8 possible outcomes, each outcome has a probability of 1/8 = 0.125.
Then, for independent outcomes like these, we can add the number of outcomes and multiply them by the probability of the outcome.
We will then have:
Event A: 2*1/8 = 1/4 = 0.25
Event B: 4*1/8 = 1/2 = 0.50
Event C: 2*1/8 = 1/4 = 0.25
Answer:
Event A --> HHH, HHT (Probability = 0.25).
Event B --> HHH, THH, HTH, HHT (Probability = 0.50).
Event C --> TTT, THT (Probability = 0.25).