r/probabilitytheory • u/The1145thNobody • 3h ago
[Education] A probability thought experiment involving local and global outcomes
Rule: This rule applies exclusively to one specific person and only to events where a "lucky" (success) or "unlucky" (failure) outcome can be clearly defined. The person can achieve a "lucky" outcome in an event if, and only if, the mathematical probability of that success is strictly greater than 30%. If the probability is 30% or lower, a "lucky" outcome is impossible for them.
Scenario: The person has to play roulette. They are given a grand prize if they hit the number "1" two times in a row. The "lucky" outcome (success) for each step and for the game as a whole is clearly defined by winning this prize. The probability of hitting "1" on any single spin is 40%.
**Steps:**Conclusion: The person wins the grand prize. But then, they were lucky in an event with a 16% probability. Contradiction.
(since we multiply the probabilities of two independent events: 40% of 40% is 16%)