Amy, Brianne, and Cedric will each choose exactly 1 container, Container X or Container Y, and then randomly pick 1...

Understanding the Question

We need to determine which container Cedric should choose to maximize his chances of getting a red marble.

Given Information:

• Container X: 3 red marbles, 10 white marbles (13 total)
• Container Y: 2 red marbles, 8 white marbles (10 total)
• Amy picks first, Brianne picks second, Cedric picks third
• Each person chooses one container and picks one marble without replacement

What We Need to Determine: Which container gives Cedric better odds of picking red?

Initially, Container X offers \(\frac{3}{13}\) chance of red (about 23%), while Container Y offers \(\frac{2}{10}\) chance of red (exactly 20%). So Container X starts slightly better. But these odds change based on what Amy and Brianne do before Cedric's turn.

For this question to be sufficient, we need to be able to definitively say whether Container X or Container Y is better for Cedric.

Analyzing Statement 1

Statement 1 tells us: Amy picked 1 red marble from Container X.

This means Container X now has:

• 2 red marbles
• 10 white marbles
• 12 marbles total

What we still don't know: What did Brianne do? Which container did she choose? What color did she pick?

Let's think through why this matters:

• If Brianne also picks from Container X and gets red → X would have only 1 red left out of 11 total
• If Brianne picks from Container Y and gets red → Y would have only 1 red left out of 9 total
• If Brianne picks white from either container → that container's red proportion stays higher

Without knowing Brianne's action, we can't determine which container offers Cedric better odds.

Statement 1 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choices A and D.

Analyzing Statement 2

Now let's forget Statement 1 completely and analyze Statement 2 independently.

Statement 2 tells us: Brianne picked 1 red marble from Container Y.

This means Container Y now has:

• 1 red marble
• 8 white marbles
• 9 marbles total

What we still don't know: What did Amy do? Which container did she choose? What color did she pick?

Here's why Amy's action matters:

• If Amy picked from Container X → X could have 2 or 3 red marbles remaining (depending on what color she picked)
• If Amy picked from Container Y and got red → Wait! This creates a problem. Container Y only started with 2 red marbles. If Amy took a red from Y first, there would be only 1 red left. But Statement 2 says Brianne picked a red from Y. This would be impossible!
• So if Statement 2 is true, Amy must have either picked from Container X, or picked white from Container Y

Even knowing this constraint, without knowing exactly what Amy did, we can't determine final probabilities for each container.

Statement 2 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice B.

Combining Statements

Now we know exactly what happened:

• Amy picked 1 red marble from Container X
• Brianne picked 1 red marble from Container Y

Current state of containers when Cedric chooses:

• Container X: 2 red marbles out of 12 total → That's \(\frac{2}{12} = \frac{1}{6}\) of the marbles
• Container Y: 1 red marble out of 9 total → That's \(\frac{1}{9}\) of the marbles

The key comparison:

• \(\frac{1}{6}\) means "one red for every six marbles"
• \(\frac{1}{9}\) means "one red for every nine marbles"

Since you'd rather have one red in every six marbles than one red in every nine marbles, Container X gives better odds. We can verify: \(\frac{1}{6} \approx 0.167\) while \(\frac{1}{9} \approx 0.111\), so \(\frac{1}{6} > \frac{1}{9}\).

Therefore, Container X gives Cedric better odds of picking a red marble.

Both statements together are sufficient.

[STOP - Sufficient!] This eliminates choice E.

The Answer: C

With both statements, we can definitively determine that Container X offers better odds (\(\frac{1}{6}\) vs \(\frac{1}{9}\)) for Cedric to pick a red marble.

Answer Choice C: "Both statements together are sufficient, but neither statement alone is sufficient."