Two full decks mixed: Draw two cards in sequence without replacement. What is the probability both drawn cards are jacks?
Aptitude
Probability
Difficulty: Medium
Choose an option
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A1/13
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B2/13
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C7/1339
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D1/169
Answer
Correct Answer: 7/1339
Explanation
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:
P(first jack) = 8/104 = 1/13P(second jack | first jack) = 7/103P(both jacks) = (1/13) * (7/103) = 7/1339Verification / 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