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statistiques 2
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stat 2 (stat 2)
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Exercice 1Permutation
9 places alignées : 9 ! = 362’880
9 places sur table ronde : 9!/9 = 8 !
Permutation (avec 8 factoriels)
5 vêtements
2 !1 !1 !1 !
2+1+1+1 -> 5 !
2!
a) Arrangement avec répétition
4^26
b) Arrangement sans répétition
26 !/22 ! = 358’800
Combinaison
a) C5,2 ; C6,3 = 5 !/2 !3 !*6!/
3 !3 !=200
b) C5,2 * (C2,0 * C4,3 + C2,1 *
C4,2) = 160
Permutation
10 ! / 2! 2! 2! 1! 1! 1! 1!
= 453’600
Quizz 2Bis
Herbivore Carnivores Omnivores
100 40 4
20 6 0
tot 120 46 4
Evènements complémentaire sont également mutuellement exclusifs
Pas complémentaire si l’intersection est vide soit -> A∩B
P. 42
Arrangement simple
A10,8 – A9,7= (10 !/2 !)-(9 !/2 !)
1er chiffre = 9 possibilités
2ème chiffre = 9 possibilités
3ème chiffre = 8 possibilités
4ème chiffre = 7 poss
8ème chiffre =3 poss
, C25,2 = 300
Combinaison
a) 7 !/4 !3 ! = 35
b) 1/35 = 0,029
L’EUROMILLION utilise le système de combinaison
Exercice 2
A.
1) Impossible ? F
2) (∩) Conjoints ? G, F
3) Certains ? J (Univers ou Ω)
4) Complémentaires ? A, B TBS BS MS TOT
5) Mutuellement exclusif ? A∩B soit (Heureux ou Malheureux)
C∩D H 100 40 0 140
D∩E M 20 6 4 30
6) A choix ? I, H
TOT 120 46 4 170
B.
a) trop précis
b) oui car on connait le nombre total des hommes
c) oui car on connait le total d’hommes et femmes
d) non car 15% des 15% des femmes absentes donc pas dans l’énoncé
e) oui
f) oui (40 tot)
g) non (pas dans l’énoncé)
h) oui car Univers donc certain
Exercice 3
P(E1)=P(E2)=… = P(E6) = 0,14= probabilité réussir P(Ebarre1)= 1-0,14=0,86 = probabilité de rater
Q1 : 0,146 = +-0
Q2 : C6,2 (6’/4’*2’) -> C6,2*0,142*0,864=0,161
Q3 : A= 0 réussi en 6 tirs, B= 1 réussi en 6 tirs -> P(au moins 2 réussi en 6 tirs) = 1-P(A) – P(B)
P(A) = 0,866= 0,404 ; P(B)= C6,1*0,141*0,865= 0,395
P(>=2x mouches en 6 tirs) = 1-0,866-(C6,1*0,14*0,865)=0,2
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