Reese, Greg, and Brad meet once a week for coffee. They each have their favorite café and, to be fair, they use randomization to choose where they will meet. Each person has a colored marble: red (R) for Reese, green (G) for Greg, and blue (B) for Brad. Each week, all three marbles are mixed well in a bag and a marble is selected. The favorite café of the person associated with the selected marble is chosen for that week’s meeting. Which of the following represents the sample space for choosing a café for the first two weeks?
Answer
A
R & G, R & B, G & R, G & B, B & R, B & G
B
R & R, R & G, R & B, R & G, G & R, G & G, G & B, B & R, B & G, B & B
C
R & R, R & G, R & B, G & R, G & G, G & B, B & R, B & G, B & B
D
R & R, R & G, R & B, G & G, G & B, B & B
Explanation
Each week, one of three cafés is chosen: Reese’s (R), Greg’s (G), or Brad’s (B). For two weeks, list every ordered pair of choices, since the first and second weeks are distinct; the same café can be chosen both weeks. This gives 3 × 3 = 9 outcomes, including R & R, G & G, and B & B. Choice C lists all nine outcomes exactly once.
AI-written and checked against the verified answer.