Finite Math Help

Question

Consider the following. (Assume that the coins are distinguishable and that what is observed are the faces or numbers that face up.)

Three coins are tossed; the result is at most one tail.

Which of the following sets of elements are included in the sample space? (Select all that apply.)

TTH HTH HHH HHT THT HTT THH TTT

Answer 1

Three coins are being tossed. All 8 possibilities are given in the question, where H means that coin was "Heads" and T means that coin was "Tails." Out of those 8 possibilities, the question is asking you to pick all the possibilities that have at most one tail. So this means we can go through the list and cross out any choice that has more than 1 T, since means more than 1 coin landed on "Tails." And that's what we do below.

TTH HTH HHH HHT THT HTT THH TTT