4 ms·

let me give a ridiculous argument that all 3 events A,B,C are equally likely: * event A involves getting one 6 from six dice * event B involves getting two

let me give a ridiculous argument that all 3 events A,B,C are equally likely: * event A involves getting one 6 from six dice * event B involves getting two 6's from twelve dice * event C involves getting three 6's from eightteen dice since all three events are in proportion, 1:6=2:12=3:18 the events themselves must all be equally likely. -------------------------------------------------------------------------------------------------------------------------------- these faulty arguments must have been thrown out all over the place in Newton's time... and I doubt many discussions today are more careful. I can imagine a room full of politicians arguing over the likelihood of a certain event and three camps emerging as to whether they feel A, B, C is more likely --- throwing away the correct mathematical argument as too complicated. -------------------------------------------- what is the correct argument anyway? For the third event C(18,3)*(1/6)^3(5/6)^(18-3) I believe as we put larger and larger numbers we do get a limit, so these numbers are tending to zero: C(6*k,k)*(1/6)^k(5/6)^(5k) ---> 1/sqrt(2*pi*(5/6)*k) ---> 0 so that event A could be the most likely. This does not sound like Isaac Newton at all.. instead more like Jacob Bernoulli

maverick_iceman 10y ago
1- {(5/6)^18 +(18(5/6)^17)/6 + 1817*(5/6)^16/72}
JadeNB 10y ago
For what it's worth, the article formalises "one 6 from 6 dice" as "at least one 6", and similarly for the other events, which throws off your probability (which works with "exactly one 6") and hence your asymptotics.
unclesaamm 10y ago
You're right about the prevalence of guesswork about probability along laypeople (and everyone until Pascal was essentially a layperson). The Emergence of Probability is a very interesting book on this topic that sketches how statistica emerged from an odd mix of intuitive advances, from places like medicine and alchemy where before statistics you had to guess whether your medicine worked.

maverick_iceman 10y ago

1- {(5/6)^18 +(18(5/6)^17)/6 + 1817*(5/6)^16/72}

JadeNB 10y ago

For what it's worth, the article formalises "one 6 from 6 dice" as "at least one 6", and similarly for the other events, which throws off your probability (which works with "exactly one 6") and hence your asymptotics.

unclesaamm 10y ago

You're right about the prevalence of guesswork about probability along laypeople (and everyone until Pascal was essentially a layperson). The Emergence of Probability is a very interesting book on this topic that sketches how statistica emerged from an odd mix of intuitive advances, from places like medicine and alchemy where before statistics you had to guess whether your medicine worked.