Math Problem Statement

A standard deck of 52 playing cards is placed facedown on a table. How many cards must you draw from the deck to be certain that you will have four kings?

Solution

To be certain that you draw all four kings from a standard deck of 52 cards, let's consider the worst-case scenario:

  1. In the worst case, you could draw all 48 non-king cards first. This leaves only the four kings in the deck.
  2. Therefore, after drawing 48 cards, you would still have no kings.
  3. By drawing four more cards, you would be guaranteed to draw the four kings.

Thus, in the worst case, you need to draw 48+4=5248 + 4 = 52 cards to be certain of having all four kings.

Answer:

You must draw 52 cards to be certain of having all four kings.

Would you like a more detailed breakdown of this reasoning?


Related Questions

  1. How many cards must you draw to ensure you have at least one king?
  2. If you only wanted two kings, how many cards would you need to draw to guarantee this?
  3. What is the minimum number of cards needed to have at least one card from each suit?
  4. If you want at least one of each rank (2 through Ace), how many cards must you draw?
  5. How many cards must you draw to ensure you have four queens?

Tip

In probability problems involving worst-case scenarios, assume the least favorable distribution of the desired outcomes. This ensures you're prepared for the least likely, but possible, situation.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Probability
Worst-case scenario analysis

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12