The Two Envelope Paradox. Should You Switch? #hanumankind #facts #growththroughfailure

Dive into the fascinating world of probability and paradoxes with our deep dive into the Two Envelopes Paradox! 🌟 In this video, we start with a clear explanation of the two envelopes and the intriguing money distribution between them. Next, we introduce the critical element: the option to switch envelopes, along with the reasoning that prompts you to consider it. Finally, we unravel the paradox itself, dissecting the flawed logic that tempts you to switch and why it defies common sense. This mind-bending topic is sure to challenge your perceptions of probability and decision-making!

🔍 Keywords: Two Envelopes Paradox, probability, decision-making, logic, switching option, flawed reasoning

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#TwoEnvelopesParadox #Probability #DecisionMaking #LogicParadox #MathematicalParadox

OUTLINE:

00:00:00 The Envelope Paradox: Should You Switch?

[ceezthemexican]

That only works with more than two options, when one options is revealed to not have the concerning prize

[thomaskaldahl]

You're incorrectly calculating expected value.

Suppose you pick an envelope with amount x. The other envelope has a 50:50 chance of having amount 2x or ½x. You incorrectly calculated the expected value using the arinhmetic mean, giving you (5/4)x in the other envelope. The arithmetic mean does NOT apply here because this is a MULTIPLICATIVE context. You should use the geometric mean, giving you an expected value of √(2x•½x) = x, agreeing with the obvious: it is not advantageous to switch.

[chrisg]

What is this "seemingly logical yet flawed reasoning"?

Very simple once spotted. Just because one envelope contains twice the other it doesn't follow that one envelope contains half or twice the other. We're now suddenly talking about 3 sums of money when before it was just 2. No need to go into probability theory, like expected value, to see that.