Urn without replacement: A bag has 8 blue and 4 white balls (12 total). Two balls are drawn without replacement. What is the probability both are blue?

Introduction / Context:
Sampling without replacement changes the denominator on the second draw. We compute the sequential probability of drawing two blue balls in a row from a finite urn.

Given Data / Assumptions:
Blue = 8, White = 4, Total = 12; draws are without replacement.

Concept / Approach:
Use sequential multiplication with conditional probability for the second draw.

Step-by-Step Solution:

Verification / Alternative check:
Combinatorial: C(8,2)/C(12,2) = 28/66 = 14/33.

Why Other Options Are Wrong:
7/33 is half the correct value; 11/33 or 2/33 do not align with either method.

Common Pitfalls:
Using 12 in the denominator for both draws (as if with replacement) or ignoring the reduced blue count after the first draw.

Final Answer:
14/33