JotD / QotD Ελληνική Λίστα Κουίζ (QotD)


Θέμα: Aeroplano (APANTHSH)



(nil): Skouteris Dimitris (dimitris(@)impact.dyn.unipg.it)
Ημερομηνία: Παρ 25 Φεβ 2005 - 15:22:46 EET

Kalhmera se olous.

As arxisw dinontas thn apanthsh : H pi0anothta einai 1/2 (50 %) oti o
Paulos 0a katsei sth swsth tou 0esh. Kai auto einai ane3arthto apo ton
ari0mo twn epivatwn (arkei, vevaia, na einai toulaxiston 2 !).

An paroume thn akoma genikoterh periptwsh opou perisseuoun n 0eseis, tote
h pi0anothta na katsei swsta o Paulos einai (n+1)/(n+2), asxeta apo ton
ari0mo twn epivatwn. Profanws auto isoutai me 1/2 gia n = 0.

0a to apodei3oume me teleia epagwgh ston ari0mo twn epivatwn, opou 0a
upo0etoume oti perisseuoun panta n 0eseis :

- An oi epivates einai 2 (h Despoina kai o Paulos !) tote profanws o
Paulos exei pi0anothta (n+1)/(n+2) na katsei sth 0esh tou (h monh
periptwsh na mhn katsei einai na katsei ekei h Despoina).

- Estw oti, an oi epivates einai ligoteroi h isoi me k, o Paulos exei
pi0anothta (n+1)/(n+2) na katsei sth 0esh tou.

- Pairnoume thn periptwsh me k+1 epivates. Uparxoun 3 upoperiptwseis :

a. H Despoina ka0etai sth swsth ths 0esh h se mia apo autes pou
perisseuoun (pi0anothta = (n+1)/(n+k+1)). Tote o Paulos 0a katsei sigoura sth
swsth tou 0esh, afou oloi oi alloi exoun ta apokommata tous (desmeumenh
pi0anothta = 1).

b. H Despoina ka0etai sth 0esh tou Paulou (pi0anothta = 1/(n+k+1)). Tote
profanws o Paulos den prokeitai na katsei sth swsth tou 0esh
(desmeumenh pi0anothta = 0).

c. H Despoina ka0etai sth 0esh enos tritou epivath X (pi0anothta
(k-1)/(n+k+1)). Tote, molis oi endiamesoi epivates (meta3u Despoinas
kai X) katsoun stis swstes tous 0eseis, arkei na vaftisoume ton epivath
X Despoina, kai to provlhma anagetai sto idio provlhma me ligoterous
epivates. O Paulos exei desmeumenh pi0anothta (n+1)/(n+2) na katsei sth
swsth tou 0esh sumfwna me thn epagwgikh mas upo0esh.

Sta0mizontas tis 3 desmeumenes pi0anothtes loipon exoume :

p = 1 * (n+1)/(n+k+1) + 0 * 1/(n+k+1) + (n+1)/(n+2) * (k-1)/(n+k+1) =

= (n+1) / (n+2).

Ara o Paulos exei panta pi0anothta (n+1)/(n+2) na katsei sth swsth 0esh,
opou n o ari0mos twn 0esewn pou perisseuoun.

(Endiaferon, e ; Valte akoma 1000 epivates kai den allazei tipota. Valte
akoma mia adeia 0esh kai h pi0anothta tinazetai apo to 1/2 sto 2/3 !).

EPITUXONTES :

Giwrgos Giaglis
George Papargiris
UnknownTechnologies (me thn extra genikeush gia tis adeies 0eseis)
maria_salonica
Miltiadis Vasilakis (aneu apodei3ews)
pak kar

Kala na pernate,

Dimitris

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