## a new Monty Hall riddle

Posted in Books, Kids, Mountains, pictures, R, Statistics, Travel with tags , , , , , , , , , on May 22, 2020 by xi'an

The Riddler was sort of feeling the rising boredom of being under lockdown when proposing the following variant to the Monty Hall puzzle:

There are zero to three goats, with a probability ¼ each, and they are allocated to different doors uniformly among the three doors of the show. After the player chooses a door, Monty opens another door hidding a goat or signals this is impossible. Given that he did open a door, what is the probability that the player’s door does not hide a goat?

Indeed, a straightforward conditional probability computation considering all eight possible cases with the four cases corresponding to Monty opening a door leads to a probability of 3/8 for the player’s door. As confirmed by the following R code:

```s=sample
m=c(0,0)
for(t in 1:1e6)m=m+(range(s(1:3,s(1:3,1)))>1)
```

## in the street for a year

Posted in Mountains, pictures, Travel, University life with tags , , , , , , , , , , on April 13, 2018 by xi'an

Just like about every year, I sent two of my pictures to the photography competition of Paris Dauphine, with not much consideration for the theme “green the future”, and was hence quite surprised to get selected this time! (Almost as much surprised as last year when an almost perfect copy of my picture of the Alcazar Baths of Lady María de Padilla got selected!) As I could travel back from Oxford to attend the opening ceremony, I went there last night, wondering at which of my pictures had been selected (Lac Pavin, Auvergne versus the Quinrang, Skye)…

And so this picture will remain exposed in the street, boulevard Lannes, for the incoming year, meaning I will cross it each time I bike to the university! The 22 other pictures were more in tune with the theme of a green future, like the winning one of a fast moving métro carriage at the station Chemin Vert. Or this simple blade of grass growing from ashes…

And thus the winner is… Continue reading