An experiment is given together with an event. find the (modeled) probability of each event, assuming that the coins are distinguishable and fair, and that what is observed are the faces uppermost. three coins are tossed; the result is at most one tail.

Saying that the result is "at most" one tail means that there can be zero or one tail.

Consider the sample space S, which is the set of all possible outcomes: S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}. Therefore: S = 8.

Now, consider the event space E, which is the set of successful outcomes: E = {TTT, TTH, THT, HTT}. Therefore: E = 4.

The probability will be:
p = E / S = 4 / 8 = 0.5

Hence, when three coins are tossed the probability that the result is at most one tail is 50%.