The 50/50 Problem You Won't Believe
Vsauce2
Aug 16, 2021 18:14
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Probability is one of the clearest, more straightforward disciplines within mathematics. Unfortunately, almost nothing in mathematics is murkier and more misleading than… probability. WHAT?!
Belgian mathematician Maurice Kraitchik posed a simple question about wagering wallets, and in doing so he revealed a paradoxical mismatch between a raw, indisputable math conclusion and common sense logic. Why does the math say one thing and reality says another? What do we do when the numbers don’t lie, but we know they aren’t telling the whole truth?
Probability density functions. Bayesian subjectivist analysis. You can put it all together and still not be able to square the math with the simple nagging logic that tells you something different.
Maybe there are some antinomical paradoxes we just have to live with. And maybe that’s okay.
*** SOURCES ***
Merryfield, K., Viet, N., & Watson, S. (1997). The Wallet Paradox. The American Mathematical Monthly, 104(7), 647-649. doi:10.2307/2975058
Carroll, M., Jones, M., & Rykken, E. (2001). The Wallet Paradox Revisited. Mathematics Magazine, 74(5), 378-383. doi:10.2307/2691032
Kraitchik, M. (1942). Mathematical Recreations. W. W. Norton.
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