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

Answer:

The second tree - diagram (with the first branch labeled H and T, and from each of those branches, there are two more branches labeled H and T) represents the sample space.

Explanation:

Step1: Understand coin - flip outcomes

A coin flip has 2 outcomes: heads (H) and tails (T).

Step2: Analyze first flip

When the coin is flipped the first time, there are two possibilities: H or T.

Step3: Analyze second flip

For each outcome of the first flip (either H or T), when the coin is flipped a second time, there are again two possibilities (H or T). So starting with H on the first flip, we can get HH or HT, and starting with T on the first flip, we can get TH or TT. The tree - diagram that shows this correctly has an initial split into H and T, and then from each of those, another split into H and T.