Multiple choice general knowledge math & puzzles

You are given an initial prize of one dollar. A coin will be tossed indefinitely until a tails occurs. Every time a heads is tossed your prize will be doubled. When a tails is tossed you walk away with whatever your prize has grown to. For example if you toss three heads and then tails you would get $1*2*2*2=$8 dollars. What is the expected return of this game?

  1. 1/2

  2. 1/4

  3. infinity

  4. 1/5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is the St. Petersburg paradox. Expected value = sum of (1/2^n × 2^n) = sum of 1 = infinity. Each term contributes $1 to the expectation. This is a famous result in probability theory showing infinite expectation from a finite-prize game.

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