Answer
$S=\{HH, HT, TH, TT \}$,
$P(HH)=P(HT)=P(TH)=P(TT)=\frac{1}{4}$.
Work Step by Step
A fair coin has two sides: head (H) or tail (T), each has the same chance $\frac{1}{2}$ to appear. For tossing two fair coins once, we can construct the sample space as $S=\{HH, HT, TH, TT \}$ and the probabilities of each outcome are: $P(HH)=P(HT)=P(TH)=P(TT)=\frac{1}{4}$.
