which tree diagram represents the sample space of this compound event?

Answer:

The first tree - diagram (the one with three main branches labeled R, B, Y and each of those branches having three sub - branches labeled R, B, Y) represents the sample space of the compound event.

Explanation:

Step1: Identify the events

The spinner has 3 colors: red (R), blue (B), yellow (Y).

Step2: Understand the compound event

The spinner is spun two times.

Step3: Analyze the sample - space requirements

For a two - spin event, starting with each of the 3 first - spin outcomes (R, B, Y), there should be 3 possible second - spin outcomes. The first tree - diagram shows this correctly as each of the R, B, Y main branches has 3 sub - branches (R, B, Y), while the second tree - diagram does not account for all possible combinations.