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rojun
@rojun@mastodon.social
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Joined March 30, 2019
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Replying to
@alisonkiddle@mathstodon.xyz
@alisonkiddle@mathstodon.xyz
Probabilities are:
(½)¹⁰ vs (⅙)⁴
For concise notation, I'll invert them:
2¹⁰ vs 6⁴
We can decompose the right side:
(2 * 3)⁴ = 2⁴ * 3⁴
We have 2s exp. so again can reduce both sides:
2⁶ vs 3⁴
Again decomposing:
2³ * 2³ = 8 * 8 vs 9 * 9
We see that the right side is bigger, so when we invert them, the left side is bigger i.e. 10 coin tosses for same side has higher probability:
(½)¹⁰ > (⅙)⁴
Replying to
@adapalmer@wandering.shop
@adapalmer@wandering.shop Oh, I thought that was in 400 BC by the plebeians of Rome
Replying to
@johncarlosbaez@mathstodon.xyz
@johncarlosbaez@mathstodon.xyz Thank you for this, it made me feel happier and hopeful amid a gloomy Monday morning.
I'm going to call this "The Earth is only slightly more dense than a flea"-diagram.