Archive for the Wines Category
trou noir
Posted in pictures, Travel, Wines with tags alcohol-free beers, can, Lac-Saint-Jean, Metabetchouan, microbrewery, Québec, Québec beers, stout, vacations on October 20, 2022 by xi'an
Sancerre
Posted in Wines with tags French wines, Loire, Sancerre, Susie Bayarri, white wine on September 20, 2022 by xi'an
Mas Foulaquier [Pic Saint-Loup]
Posted in Wines with tags French wines, grenache, Languedoc wines, Mas Foulaquier, Pic Saint Loup, red wine, Syrah, tanin on August 20, 2022 by xi'an
microbrasserie du Lac-Saint-Jean
Posted in Wines with tags craft beer, Lac-Saint-Jean, microbrewery, Québec, Saint-Gédéon, vacations on July 20, 2022 by xi'an
Goats do room
Posted in Books, Kids, R, Statistics, Wines with tags Aosta, bouquetins, Goat-Roti, Goats do roam, Italian Alps, mathematical puzzle, R, ranking, riddle, South African wines, StackExchange, The Riddler, wines on July 16, 2022 by xi'an
The riddle of the week is about 10 goats sequentially moving to their room, which they have chosen at random and independently (among ten rooms), unless another goat already occupies the room, in which case they move to the first free room with a higher number or fail. What is the probability that all goats end up in a room?
Coding the experiment is straightforward:
g=sample(1:N,N,rep=TRUE)
o=0*g
for(i in 1:N){
if(min(o[g[i]:N])){f=f+1;break()
}else{
o[min(which(!o[g[i]:N]))+g[i]-1]=1
}}}
returning an estimated probability of approximately 0.764.
As I had some free time during the early mornings at ISBA 2022, I tried to reformulate the question as a continuous event on uniform order statistics, turning to be at most one uniform larger than (N-1)/N, at most two larger than (N-2)/N, and so on… Asking the question on math.stackexchange quickly produced an answer that reversed engineered my formulation back to the goats (or parking lot), with a generic probability of
which of course coincides with the Monte Carlo approximation!
As an aside, I once drank South-African wines named Goats-do-Roam and Goat-Roti at my friends Jim and Maria’s place, and they were quite enjoyable!
Xi'an's Og 