Spades are Rich

What this expected-value card-game question tests

This is an easy probability question that asks you to compute the expected value of a randomly drawn card from a standard deck, where cards have both a nominal value and a suit-based modifier. It is a straightforward warm-up on linearity of expectation and the law of total probability.

To solve problems in this category, you partition the deck by the relevant property (in this case, suit), assign values to each card according to the rules given, and then average across all 52 cards. The key insight is recognizing that you can either compute the full weighted sum directly, or use symmetry to simplify the calculation. Interviewers use these questions to verify that you can set up a probability model correctly and avoid arithmetic mistakes under time pressure.

• Partitioning outcome spaces
• Discrete expectation via enumeration
• Symmetry and conditional expectation