How do two independent coin tosses give four possible outcomes?

A sample space lists all possible outcomes of a model. For two coin tosses, an outcome records the first result and then the second. HH, HT, TH and TT are four different ordered outcomes. HT and TH each contain one head, but they describe different sequences.

Each toss is fair in this model, so heads and tails each have probability one half. The tosses are also independent: learning the first result does not change the probability of the second. That is why both second-stage branches remain one half after either first-stage result.

The probability of a particular complete path multiplies its branch probabilities. Thus HH has probability one half times one half, or one quarter. The same calculation gives one quarter for each other leaf. The four leaf probabilities add to one, covering the entire sample space.

An event can contain more than one leaf. Both heads contains only HH and has probability one quarter. Exactly one head contains HT and TH and has probability one half. These are statements about the stated model, not promises about the results of a small number of physical tosses.