At least one matching pair in three cards

Draw three cards from a shuffled standard deck. What is the probability that at least two of them share a rank? Give a decimal to four places.

Show hints (2)+
  1. Use the complement: probability all three cards have distinct ranks.
  2. Chain the conditionals: 1485144501 \cdot \tfrac{48}{51} \cdot \tfrac{44}{50}, then subtract from 1.

Answer

Reveal answer →

0.1718 (± 0.005)

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Asked at: Game-Based Aptitude, EV & Betting Games

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