Timeline for How many tries to roll a 6?
Current License: CC BY-SA 3.0
15 events
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| Dec 5, 2017 at 2:40 | comment | added | Silverfish | An alternative argument: the probability of landing on one of $\{1,3,5,6\}$ is $p = \frac 4 6= \frac 2 3$. Your answer gives the intuition for why we seek the the expected number of rolls up to and including the first appearance of $\{1,3,5,6\}$, which is $1/p = \frac 3 2$ - using the well-known formula for the expected number of independent trials up to and including the first "success", where $P(\text{success})=p$. (This is the same formula that gives the expected number of rolls up to and including the first six as $1 \div \frac 1 6 = 6$, the example given in the question text.) | |
| Dec 3, 2017 at 1:16 | history | undeleted | Gareth McCaughan♦ | ||
| Dec 3, 2017 at 1:15 | history | post merged (destination) | |||
| Sep 20, 2017 at 4:35 | history | edited | humn | CC BY-SA 3.0 |
sheesh, "expectancy" does not mean "expected value" but "expectation" does
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| Sep 20, 2017 at 1:58 | history | bounty ended | Deusovi♦ | ||
| Sep 19, 2017 at 20:06 | comment | added | humn | I might understand your comments even better now, @Artur K and $\raise-.2ex\unicode{x40}$Deusovi, and have added a Note about them. | |
| Sep 19, 2017 at 20:04 | history | edited | humn | CC BY-SA 3.0 |
note from comments about loose ends
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| Sep 17, 2017 at 23:51 | history | edited | humn | CC BY-SA 3.0 |
correct the probability of a sequence being a 1-long lone 6
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| Sep 17, 2017 at 23:40 | comment | added | Deusovi♦ | "An infinite comparison comes out perfectly equal"? Only in terms of cardinality. In terms of natural density (which I'd argue is more natural (pun completely intended) in this case), the natural density of the primes is 0, which seems perfectly consistent with disparities increasing as $n\to\infty$. | |
| Sep 15, 2017 at 21:01 | history | edited | humn | CC BY-SA 3.0 |
notes section, touchup
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| Sep 14, 2017 at 19:23 | comment | added | humn | True about not treating infinity rigorously here, @Artur Kirkoryan. I wanted to disagree but remembered the simple example of comparing the population counts of primes versus whole numbers. Finite comparisons produce increasingly large disparities in favor of wholes whereas an infinite comparison comes out perfectly equal. | |
| Sep 14, 2017 at 19:10 | comment | added | Puzzle Prime | This is very nice analysis and I upvoted the answer, but I am not convinced the argument is very rigorous. We still have to argue that the various halted 2-4 sequences are represented the same way in the long term, and justify taking T to infinity. I assume there is a theorem which states something like this, e.g. "if we have a sequence of experiments one after another, grouped by outcomes, then the statistical length of the experiment in group X, converges to the truth average, under certain conditions". Once again, I like this argument, but I think I like your first solution more:) | |
| Sep 12, 2017 at 16:36 | history | edited | humn | CC BY-SA 3.0 |
last-minute italiization of randomly unitalicized Ts
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| Sep 12, 2017 at 16:26 | comment | added | Deusovi♦ | Wow, what a brilliant solution! | |
| Sep 12, 2017 at 16:17 | history | answered | humn | CC BY-SA 3.0 |