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I don't know why I started this discussion... but...

If you have any mathematical paradoxes you know, feel free to post them here. This could get interesting...

2 years, 6 months ago

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1. A jackpot is currently worth $$1$$ dollar. Every time I toss a head on a fair coin, the jackpot doubles, but when I toss a tail, the game ends and I take home the jackpot. How much should I be willing to pay to play this game?

2. I have two envelopes, and am told that one of them has twice as much cash as the other. I open Envelope 1 up. Should I stick to it or switch? Wait, but the envelopes are the same. Why is it that I should always switch to Envelope 2?

3. In a casino game, a random number $$x$$ in the interval $$(0, 1)$$ is generated on a calculator, and I win $$\frac{1}{x}$$ dollars. How much should I be willing to pay to play this game?

4. Player A and Player B are in a 100 meter race. Player A is at the 50 meter mark, walking at $$1$$ $$m/s$$. Player B is at the 20 meter mark, sprinting at $$10$$ $$m/s$$. When Player B reaches the 50 meter mark, player A would've covered some distance by then. Then, when Player B reaches that point, Player A would've walked some more, and so on. Therefore, Player B will never catch up with Player A, and lose the race.

- 2 years, 6 months ago

I am also interested in #2. I would think the probability would be 50 50.

- 2 years, 6 months ago

Thank you for these!!!

- 2 years, 6 months ago

I think I have an answer to the 4th one A would be moving but will cover less distance than B in the same time interval......... Therefore at some time B will cross A.

- 2 years, 6 months ago