The Two Jars and Marbles Puzzle

A king gives you two jars and 100 marbles—50 white and 50 black. He will randomly select one jar, then pick one marble from it.

  • If the marble is white, you win freedom.
  • If the marble is black, you are executed.

How should you distribute the marbles to maximize your survival?

Put 1 white marble in one jar and the remaining 99 marbles (49 white + 50 black) in the other jar.


Explanation:

  • The king has a 50% chance of picking either jar.
  • If he picks Jar 1 (1 white marble)100% survival.
  • If he picks Jar 2 (49 white + 50 black) → You have a 49/99 ≈ 49.49% chance of survival.

Total Probability of Survival:

50% × 100% + 50% × 49.49% = 50% + 24.75% = 74.75%

This setup gives you a 74.75% chance of survival, the highest possible.

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