Question

lee picks one marble from a bag and flips this coin once. there is 1 red marble, 1 yellow marble, 1 blue marble, and 1 purple marble. which tree - diagram represents the sample space of this compound event?

Explanation:

Step1: Analyze the compound - event

The compound event is picking a marble (4 options: red - R, yellow - Y, blue - B, purple - P) and flipping a coin (2 options: heads - H, tails - T).

Step2: Check the structure of the tree - diagram

The first level of the tree - diagram should have 4 branches for the 4 marbles. Each of these branches should then split into 2 branches for the 2 coin - flip results.

Step3: Evaluate the given diagrams

The first diagram has incorrect structure as the coin - flip branches are not correctly attached to the marble branches. The second diagram has an incorrect start with 'Y' and 'B' as the top - level branches and also incorrect combinations. The third diagram has the correct structure with 4 initial branches for marbles (R, Y, B, P) and each of those branches splitting into 2 branches for H and T.

Answer:

The third tree - diagram represents the sample space of this compound event.