Answer:
see attached
Explanation:
You want the table filled in with the appropriate outcomes identified and their respective probabilities shown.
Outcomes
As with a lot of math, this is about reading comprehension, pattern matching, and counting.
The problem statement tells you the meaning of the letter combinations, THT, for example. This one means the first and last coin tosses were heads, and the second toss resulted in tails.
The first part of the problem asks you to identify the outcomes that have a first and last toss of heads. This one (THT) would be one of those. The other one would be TTT. You are asked to check those boxes in the table, as we have done in the attachment.
Similarly, the other lines in the table require you to understand the description of the outcomes of interest, and match the description to the pattern of T and H shown at the head of the columns.
Probability
There are 8 possible outcomes. The probability of one of them is 1/8. The probability of n of them is n/8. Hence, the probability of first and last tosses being Tails is 2/8 = 1/4, because only 2 of the 8 outcomes match that description.
The other probabilities are shown in the attachment.