Difficulty: Easy
Correct Answer: 14/33
Explanation:
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:
P(first blue) = 8/12 = 2/3P(second blue | first blue) = 7/11P(both blue) = (2/3) * (7/11) = 14/33Verification / 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
Discussion & Comments