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

Answer:

The correct tree diagram starts with the first flip branching into H (Head) and T (Tail), and each of these branches further splits into H and T for the second flip, resulting in four end branches: HH, HT, TH, TT.

Explanation:

Step 1: Identify possible outcomes for the first flip

The first coin flip has 2 outcomes: H, T.

Step 2: Branch second flip outcomes from each first flip result

For each outcome of the first flip (H or T), the second flip again has 2 outcomes (H, T), creating 2×2=4 total outcomes.

Step 3: Match the structure

The correct tree diagram must show two initial branches (first flip: H, T) with two sub-branches each (second flip: H, T), representing all 4 possible outcomes (HH, HT, TH, TT).