Two full decks mixed: Draw two cards in sequence without replacement. What is the probability both drawn cards are jacks?

Introduction / Context:When two standard decks (2 × 52 = 104 cards) are thoroughly shuffled, there are 8 jacks total. We draw two cards sequentially without replacement and want both to be jacks.

Given Data / Assumptions:

• Total cards = 104; total jacks = 8.
• Sampling without replacement; order matters only in probability multiplication.

Concept / Approach:Use sequential probability: P(first jack) × P(second jack | first jack). Multiply numerators and denominators carefully to avoid arithmetic slips.

Step-by-Step Solution:

Verification / Alternative check:Combinatorial form: C(8,2)/C(104,2) = [28]/[5356] = 7/1339, same result.

Why Other Options Are Wrong:

• 1/13 or 2/13 ignore the second conditional step.
• 1/169 assumes replacement or independence that does not hold here.

Common Pitfalls:Using 52 instead of 104; forgetting there are 8 jacks; assuming replacement.

Final Answer:7/1339