sam flips this coin three times. which tree diagram represents the sample space of this compound event?

Explanation:

Step1: Analyze coin - flip outcomes

Each coin - flip has 2 outcomes (heads H or tails T).

Step2: Determine sample - space for 3 flips

For the first flip, there are 2 branches (H and T). For each of these branches, the second flip has 2 sub - branches (H and T), and for each of these sub - branches, the third flip has 2 sub - sub - branches (H and T). The given tree diagram with 3 levels of branching, where at each level the number of branches doubles, correctly represents the sample space of 3 coin flips. The first level represents the first flip, the second level represents the second flip for each outcome of the first flip, and the third level represents the third flip for each outcome of the first two flips.

Answer:

The provided tree diagram represents the sample space of the compound event of flipping a coin three times.