vince spins this spinner two times. which tree diagram represents the sample space of this compound event?

Explanation:

Step1: Identify possible outcomes for first - spin

The first spin can result in yellow (Y), purple (P), or green (G).

Step2: Identify possible outcomes for second - spin

For each outcome of the first spin, the second spin can also result in yellow (Y), purple (P), or green (G). If the first spin is Y, the second - spin possibilities are Y, P, G. If the first spin is P, the second - spin possibilities are Y, P, G. If the first spin is G, the second - spin possibilities are Y, P, G. The correct tree - diagram should have three branches coming out from the starting point for the first spin (Y, P, G), and then for each of those branches, three more branches (Y, P, G) for the second spin. The second tree - diagram represents the sample space correctly.

Answer:

The second tree - diagram (the one with three main branches for the first spin: Y, P, G and for each of those, three sub - branches Y, P, G)