a
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High
School
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Grade 11 - STMG
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Ressource
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4
3
2
1
Grade 11 - STMG
/ Probability
32 exercises (including 31 corrected)
a
Counts
(1 exercice)
Set
(3 exercices)
Double-entry table
(3 exercices)
Non-equiprobable situation
(1 exercice)
Choice trees
(5 exercices)
Probability tree
(3 exercices)
Binomial law
(2 exercices)
Binomial law and expectation
(3 exercices)
Binomial law and representation
(2 exercices)
Binomial law and calculator
(6 exercices)
Fluctuation interval
(2 exercices)
image PNG : /home/_math/_exercice/d7/7852/metapost/a.png
As
As
As
As
R
R
R
R
D
D
D
D
V
V
V
V
10
10
10
10
9
9
9
9
8
8
8
8
7
7
7
7
♥
♦
♠
♣
A
B
A
A
B
B
A
B
A
B
A
B
A
B
A
B
1.
Counts
E.7653
An
urn
con
tains
12
white
balls,
5
blac
k
balls
and
8
blue
balls
indistinguishable
b
y
touc
h.
Consider
our
univ
erse
of
exp
erience
comp
osed
of
the
follo
wing
three
elemen
tary
ev
en
ts
:
A
:
ˇ
The
ball
dra
wn
is
blanc
he
ı
B
:
ˇ
The
ball
dra
wn
is
noire
ı
C
:
ˇ
The
ball
dra
wn
is
bleue
ı
Complete
the
table
b
elo
w,
to
the
nearest
h
undredth,
repre-
sen
ting
the
probabilit
y
distribution
of
our
exp
erimen
t
:
X
A
B
C
P
(
X
)
2.
Set
E.7654
The
table
b
elo
w
pro
vides
an
o
v
erview
of
daily
newspap
er
readership
in
F
rance,
based
on
a
sample
of
800
p
eople
surv
ey
ed
in
2005
.
Ev
ery
da
y
or
almost
ev
ery
da
y
Once
or
t
wice
a
w
eek
Only-
during
certain
p
erio
ds
Rarely
Nev
er
T
otal
F
armers
op
erators
1
10
2
8
79
100
Craftsmen,
shopk
eep
ers
,
managers
of
companies
11
11
5
7
66
100
Executiv
es
17
16
10
18
39
100
Professions
in
ter-
media
8
15
7
15
55
100
Emplo
y
ees
6
7
4
9
74
100
W
ork
ers
(including
agricultural)
4
5
3
5
83
100
Retirees
6
7
2
6
79
100
Others
inactiv
e
5
9
4
9
73
100
T
otal
in
w
orkforce
58
80
37
77
548
800
P
ercen
tages
of
total
7.25
%
10
%
4.625
%
In
this
exercise,
results
will
b
e
giv
en
in
decimal
form
and
rounded
to
the
nearest
0.001
.
P
art
A.
1
The
last
ro
w
of
the
table
b
elo
w
represen
ts
the
share
of
eac
h
category
in
relation
to
the
total
sample.
Calculate
the
missing
v
alues
in
this
last
ro
w.
2
Giv
e
the
probabilit
y
that
a
p
erson
c
hosen
at
random
from
among
the
executiv
es
nev
er
reads.
P
art
B.
W
e
randomly
select
one
p
erson
from
this
sample
of
800
p
eople.
In
this
section,
w
e
note
the
follo
wing
ev
en
ts
:
J
Ev
en
t
:
ˇ
The
p
erson
selected
nev
er
reads
ı
;
O
Ev
en
t
:
ˇ
the
p
erson
c
hosen
is
a
w
ork
er
ı.
1
Calculate
the
probabilit
y
of
ev
en
t
J
and
the
probabilit
y
of
ev
en
t
O
.
2
Calculate
the
probabilit
y
of
ev
en
t
J
∩
O
.
3
Calculate
the
probabilit
y
of
ev
en
t
J
∪
O
E.7657
A
random
exp
erimen
t
in
v
olv
es
randomly
dra
wing
a
card
from
a
dec
k
of
32
cards.
1
Determine
the
probabilities
of
the
fol-
lo
wing
ev
en
ts
:
A
:
ˇ
The
card
dra
wn
is
a
pique
ı
;
B
:
ˇ
The
card
dra
wn
is
a
figure
ı
;
C
:
ˇ
The
card
dra
wn
is
noire
ı
;
D
:
ˇ
The
card
dra
wn
is
v
alet
ı
;
2
Determine
the
probabilities
of
the
follo
wing
ev
en
ts
:
a
A
∩
B
b
A
∩
C
c
A
∪
B
d
B
∪
C
e
C
∩
D
f
C
∪
D
E.7659
Belo
w
are
represen
ted
the
univ
erse
Ω
of
a
random
exp
erimen
t
and
t
w
o
ev
en
ts
A
and
B
from
Ω
.
F
or
eac
h
of
the
represen
tations
b
elo
w,
hatc
h
the
requested
set.
3.
Double-entry
table
h
ttps:/
/c
hingmath.fr
chapExoCorrec/7653
sacados/7653
chapExoCorrec/7654
sacados/7654
chapExoCorrec/7657
sacados/7657
As
As
As
As
R
R
R
R
D
D
D
D
V
V
V
V
10
10
10
10
9
9
9
9
8
8
8
8
7
7
7
7
♥
♦
♠
♣
chapExoCorrec/7659
sacados/7659
A
B
A
A
B
B
A
B
A
B
A
B
A
B
A
B
1
1
2
2
3
3
4
4
5
5
6
6
Bleu
Rouge
E.11392
The
sc
ho
ol
administration
tak
es
sto
c
k
of
the
studen
ts
enrolled
in
the
half-b
oard
program
:
The
sc
ho
ol
has
852
studen
ts
;
In
total,
there
are
213
studen
ts
enrolled
in
the
ˇ
da
y
stu-
den
t
ı
;
program
F
or
girls,
123
girls
are
enrolled
in
the
ˇ
da
y
stu-
den
t
ı
program
and
312
are
enrolled
in
the
half-b
oard
program
1
Complete
the
table
b
elo
w
:
Bo
ys
Filles
T
otal
Da
y
studen
t
Half-b
oard
T
otal
2
A
studen
t
is
c
hosen
at
random
from
the
list
of
studen
ts
:
a
What
is
the
probabilit
y
that
the
studen
t
is
a
girl?
b
What
is
the
probabilit
y
that
the
studen
t
is
a
half-
b
oarder?
c
Kno
wing
that
the
studen
t
is
a
b
o
y
,
what
is
the
proba-
bilit
y
that
he
is
a
da
y
studen
t?
E.11427
W
e
are
in
terested
in
three
sixth-grade
classes
at
a
sc
ho
ol.
V
olleyball
and
so
ccer
are
offered
as
ex-
tracurricular
activities
and
together
ha
v
e
354
mem
b
ers.
Here
is
some
additional
information
that
has
b
een
gathered
:
76
girls
ha
v
e
signed
up
for
v
olleyball
There
are
132
mem
b
ers
in
the
v
olleyball
club.
There
are
238
b
o
ys.
1
Complete
the
table
:
V
olleyball
So
ccer
T
otal
Bo
ys
Girls
T
otal
2
W
e
randomly
select
a
sixth
grader
:
a
What
is
the
probabilit
y
that
this
studen
t
pla
ys
v
olley-
ball?
b
What
is
the
probabilit
y
that
this
studen
t
is
a
girl?
c
Kno
wing
that
the
studen
t
c
hosen
is
a
b
o
y
,
what
is
the
probabilit
y
that
he
pla
ys
so
ccer?
E.11618
On
s’in
téresse
à
trois
classes
de
sixièmes
d’un
établissemen
t
scolaire.
Le
V
olley-ball
et
le
F
o
otball
son
t
prop
osés
en
activité
extra-scolaire
et
regroup
en
t
à
eux
deux
354
adhéren
ts.
V
oici
quelques
informations
complémen
taires
recueillies
:
76
filles
se
son
t
inscrites
au
V
olley-Ball.
Le
V
olley-Ball
compte
132
adhéren
ts.
Les
garçons
son
t
au
nom
bre
de
238.
1
Compléter
le
tableau
:
V
olley-ball
F
o
otball
T
otal
Garçons
Filles
T
otal
2
On
c
hoisit
au
hasard
un
élèv
e
de
sixième
:
a
Quelle
est
la
probabilité
que
cet
élèv
e
pratique
le
V
olley-ball
?
b
Quelle
est
la
probabilité
que
cet
élèv
e
soit
une
fille
?
c
Sac
han
t
que
l’élèv
e
c
hoisi
est
un
garçon,
quelle
est
la
probabilité
qu’il
pratique
le
F
o
otball
?
4.
Non-e
quipr
ob
able
situation
E.11509
A
random
exp
erimen
t
con-
sists
in
rolling
t
w
o
dice,
red
and
blue,
with
six
faces
sim
ultaneously
and
considering
the
sum
ob-
tained
b
y
these
t
w
o
dice.
The
dice
are
assumed
to
b
e
p
erfectly
balanced.
1
Describ
e
the
univ
erse
of
p
ossible
outcomes.
2
a
Complete
the
ta-
ble
b
elo
w
:
h
ttps:/
/c
hingmath.fr
chapExoCorrec/11392
sacados/11392
chapExoCorrec/11427
sacados/11427
chapExoCorrec/11618
sacados/11618
chapExoCorrec/11509
sacados/11509
1
1
2
2
3
3
4
4
5
5
6
6
Bleu
Rouge
Evènements
élémentaires
NN
N
NN
N
NB
B
N
NN
N
NN
N
NB
B
N
BN
N
BN
N
BB
B
B
1
e
r
tirage
2
e
tirage
R
R
B
R
R
R
B
R
R
R
B
B
Représentation 1
R
B
R
R
B
R
R
R
B
Représentation 2
V
2
F
2
F
2
F
2
V
1
V
2
F
2
F
2
F
2
F
1
V
2
F
2
F
2
F
2
F
1
V
2
F
2
F
2
F
2
F
1
a
Determine
the
probabilit
y
la
w
asso
ciated
with
this
random
exp
erimen
t.
5.
Choic
e
tr
e
es
E.7655
An
urn
con
tains
t
w
o
blac
k
balls
and
one
white
ball
;
the
game
is
pla
y
ed
with
the
ball
b
eing
returned
:
i.e.,
once
the
ball
has
b
een
dra
wn,
it
is
returned
to
the
urn
b
efore
the
next
dra
w.
Here’s
a
decision
tree
based
on
the
dra
wing
of
t
w
o
balls
:
1
T
aking
in
to
accoun
t
the
order
in
whic
h
the
balls
are
dra
wn,
what
is
the
p
ossible
n
um
b
er
of
differen
t
dra
ws?
2
Determine
the
probabilit
y
of
the
follo
wing
ev
en
ts
:
a
A
:
ˇ
The
first
ball
dra
wn
is
blanc
he
ı.
b
B
:
ˇ
The
t
w
o
balls
dra
wn
are
différen
tes
ı
colors.
c
C
:
ˇ
The
second
ball
is
a
noire
ı
ball.
3
Giv
e
the
probabilities
of
the
follo
wing
ev
en
ts
:
a
A
∩
B
b
A
∩
C
c
A
∪
C
E.7662
An
urn
con
tains
t
w
o
red
balls
and
one
blue
ball
indistinguishable
b
y
touc
h.
Using
this
urn,
w
e
construct
t
w
o
sets
:
W
e
dra
w
a
first
ball
from
the
urn,
then
without
putting
it
bac
k,
w
e
dra
w
a
second
ball.
A
first
ball
is
dra
wn
from
the
urn,
its
color
observ
ed
and
then
returned
to
the
urn.
A
second
ball
is
then
dra
wn.
In
b
oth
games,
the
game
is
considered
w
on
if
the
t
w
o
balls
dra
wn
are
of
the
same
color.
The
t
w
o
c
hoice
trees
b
elo
w
are
prop
osed
:
1
Asso
ciate
with
eac
h
of
the
games
its
represen
tation
in
the
form
of
a
c
hoice
tree.
2
Determine
the
probabilit
y
of
winning
for
eac
h
of
its
games.
E.7658
A
QCM
(multiple-choic
e
questionnair
e)
is
prop
osed
to
studen
ts
:
it
comprises
t
w
o
questions
and
four
answ
ers
are
prop
osed,
only
one
of
whic
h
is
correct.
W
e
wish
to
study
the
p
ercen
tage
of
success
in
this
MCQ
if
the
studen
ts
answ
er
it
completely
at
random
;
w
e
then
assume
that
the
answ
ers
giv
en
to
eac
h
of
the
questions
are
indep
en-
den
t
of
eac
h
other.
W
e
note
:
F
i
:
ˇ
The
answ
er
pro
vided
to
question
i
is
fausse
ı
;
V
i
:
ˇ
The
answ
er
pro
vided
to
the
question
i
is
vraie
ı
;
Here
is
the
c
hoice
tree
asso
ciated
with
this
situation
:
Consider
the
random
exp
erimen
t
of
randomly
selecting
the
answ
ers
to
these
t
w
o
questions
1
Giv
e
the
probabilit
y
of
obtaining
the
t
w
o
correct
answ
ers.
2
Giv
e
the
probabilit
y
of
obtaining
only
one
correct
answ
er.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/7655
sacados/7655
Evènements
élémentaires
NN
N
NN
N
NB
B
N
NN
N
NN
N
NB
B
N
BN
N
BN
N
BB
B
B
1
e
r
tirage
2
e
tirage
chapExoCorrec/7662
sacados/7662
R
R
B
R
R
R
B
R
R
R
B
B
Représentation 1
R
B
R
R
B
R
R
R
B
Représentation 2
chapExoCorrec/7658
sacados/7658
V
2
F
2
F
2
F
2
V
1
V
2
F
2
F
2
F
2
F
1
V
2
F
2
F
2
F
2
F
1
V
2
F
2
F
2
F
2
F
1
N
NN
B
NB
N
N
NN
B
NB
N
N
BN
N
BN
B
1
2
3
5
4
6
Urne
B
Urne
A
2
1
3
2
1
4
2
1
5
2
1
6
1
2
2
5
6
4
Urne
B
Urne
A
V
F
F
F
V
V
F
F
F
F
V
F
F
F
F
V
F
F
F
F
V
V
F
F
F
V
V
F
F
F
F
V
F
F
F
F
V
F
F
F
F
F
V
F
F
F
V
V
F
F
F
F
V
F
F
F
F
V
F
F
F
F
F
V
F
F
F
V
V
F
F
F
F
V
F
F
F
F
V
F
F
F
F
F
1
4
1
4
1
4
V
3
4
F
V
3
4
1
4
V
3
4
F
F
V
3
4
1
4
1
4
V
3
4
F
V
3
4
1
4
V
3
4
F
F
F
E.11510
An
urn
con
tains
t
w
o
blac
k
balls
and
one
white
ball
;
the
game
consists
of
extracting
t
w
o
balls
from
the
urn
without
deliv
ery
:
the
first
ball
dra
wn
will
not
b
e
returned
to
the
urn.
Opp
osite
is
a
c
hoice
tree
repre-
sen
ting
the
dra
ws
in
this
game.
1
T
aking
in
to
accoun
t
the
order
in
whic
h
the
balls
are
dra
wn,
what
is
the
p
ossible
n
um
b
er
of
differen
t
dra
ws?
2
Determine
the
probabilit
y
of
the
follo
wing
ev
en
ts
:
a
A
:
ˇ
The
first
ball
dra
wn
is
blanc
he
ı.
b
B
:
ˇ
The
second
ball
dra
wn
is
blanc
he
ı.
c
C
:
ˇ
The
t
w
o
balls
dra
wn
are
distinctes
ı
colors.
3
Giv
e
the
probabilities
of
the
follo
wing
ev
en
ts
:
a
A
∩
B
b
A
∩
C
c
C
E.11619
On
considère
deux
urnes
con
tenan
t
des
b
oules
sur
lesquelles
est
inscrit
un
c
hiffre.
L’exp
érience
aléa-
toire
consiste
à
tirer
une
b
oule
au
hasard
dans
l’urne
A,
puis
une
b
oule
au
hasard
dans
l’urne
B
et
à
faire
la
somme.
1
V
oici
le
con
ten
u
de
l’urne
:
On
asso
cie
à
cette
exp
érience
l’arbre
de
c
hoix
:
Quelle
est
la
probabilité
d’obtenir
la
somme
6
?
2
On
mo
difie
les
urnes
:
a
Construire
l’arbre
de
c
hoix
corresp
ondan
t
à
cette
ex-
p
érience.
b
Quelle
est
la
probabilité
d’obtenir
la
somme
7
?
6.
Pr
ob
ability
tr
e
e
E.7656
Consider
a
m
ultiple-c
hoice
questionnaire
consisting
of
3
questions,
eac
h
offering
4
answ
ers,
only
one
of
whic
h
is
correct.
A
random
exp
erimen
t
is
created
b
y
asking
participan
ts
to
answ
er
the
questions
in
the
form
at
random.
This
situation
is
represen
ted
b
y
the
decision
tree
b
elo
w
:
1
Complete
the
probabilit
y
table
b
elo
w
:
k
0
1
2
3
Probabilit
y
of
obtaining
k
correct
answ
ers
Note
that
for
eac
h
m
ultiple-c
hoice
question,
the
probabilit
y
of
getting
a
correct
answ
er
is
1
4
and
a
wrong
answ
er
is
3
4
.
W
e
simplify
the
decision
tree
with
the
probabilit
y
tree
b
elo
w
:
W
e
w
an
t
to
find
the
results
of
question
1
using
this
proba-
h
ttps:/
/c
hingmath.fr
chapExoCorrec/11510
sacados/11510
N
NN
B
NB
N
N
NN
B
NB
N
N
BN
N
BN
B
chapExoCorrec/11619
sacados/11619
1
2
3
5
4
6
Urne
B
Urne
A
2
1
3
2
1
4
2
1
5
2
1
6
1
2
2
5
6
4
Urne
B
Urne
A
chapExoCorrec/7656
sacados/7656
V
F
F
F
V
V
F
F
F
F
V
F
F
F
F
V
F
F
F
F
V
V
F
F
F
V
V
F
F
F
F
V
F
F
F
F
V
F
F
F
F
F
V
F
F
F
V
V
F
F
F
F
V
F
F
F
F
V
F
F
F
F
F
V
F
F
F
V
V
F
F
F
F
V
F
F
F
F
V
F
F
F
F
F
1
4
1
4
1
4
V
3
4
F
V
3
4
1
4
V
3
4
F
F
V
3
4
1
4
1
4
V
3
4
F
V
3
4
1
4
V
3
4
F
F
F
E
S
E
S
E
S
E
S
E
S
E
S
E
S
E
S
E
S
E
S
E
S
E
S
E
S
E
S
N
N
N
B
N
N
N
N
B
N
N
N
N
B
N
N
N
N
B
B
N
N
N
B
B
N
N
N
N
B
B
N
N
N
N
B
B
N
N
N
N
B
B
B
N
N
N
B
B
B
bilit
y
tree
:
2
a
Whic
h
calculation,
using
the
data
from
the
tree
b
e-
lo
w,
allo
ws
us
to
find
the
probabilit
y
of
getting
3
cor-
rect
answ
ers
to
Q
.
C
.
M
.
?
b
Whic
h
calculation,
using
the
data
from
the
tree
b
elo
w,
allo
ws
us
to
find
the
probabilit
y
of
obtaining
0
correct
answ
ers
to
Q
.
C
.
M
.
?
c
Whic
h
calculation,
using
the
data
from
the
tree
b
elo
w,
allo
ws
us
to
find
the
probabilit
y
of
obtaining
1
correct
answ
ers
to
Q
.
C
.
M
.
?
E.7670
Consider
a
Bernoulli
sc
heme
with
pa-
rameters
3
and
0.4
.
1
Complete
the
probabilit
y
tree
b
elo
w
:
2
Ho
w
man
y
outcomes
do
es
this
random
exp
erimen
t
ha
v
e?
3
Determine
the
probabilit
y
of
obtaining
3
success.
4
a
Ho
w
man
y
outcomes
represen
t
2
success?
b
Determine
the
probabilit
y
of
obtaining
2
success
in
this
random
exp
erimen
t.
E.7671
Consider
a
Bernoulli
sc
heme
with
pa-
rameters
4
and
0.4
.
1
Complete
the
probabilit
y
tree
b
elo
w
:
2
Ho
w
man
y
outcomes
do
es
this
random
exp
erimen
t
ha
v
e?
3
Determine
the
probabilit
y
of
obtaining
4
success.
4
a
Ho
w
man
y
outcomes
represen
t
3
success?
b
Determine
the
probabilit
y
of
obtaining
3
success
in
this
random
exp
erimen
t.
7.
Binomial
law
E.7681
1
There
are
four
balls
in
an
urn
:
three
blac
k
balls
and
one
white
ball.
T
w
o
balls
are
dra
wn
successiv
ely
from
this
urn,
with
deliv
ery
.
The
c
hoice
tree
b
elo
w
illustrates
all
the
elemen
tary
ev
en
ts
in
this
random
exp
erimen
t
:
a
Construct
the
asso
ciated
probabilit
y
tree
b
Note
X
the
random
v
ariable
asso
ciating
the
n
um
b
er
of
white
balls
dra
wn.
Determine
the
follo
wing
probabili-
ties
:
P
X
=
0
;
P
X
=
2
2
In
an
urn
are
fiv
e
balls
:
three
blac
k
balls
and
t
w
o
white
balls.
T
w
o
balls
are
dra
wn
successiv
ely
from
this
urn,
with
deliv
ery
.
The
c
hoice
tree
b
elo
w
illustrates
all
the
elemen
tary
ev
en
ts
in
this
random
exp
erimen
t
:
a
Construct
the
asso
ciated
probabilit
y
tree
b
Note
X
the
random
v
ariable
asso
ciating
the
n
um
b
er
of
white
balls
dra
wn.
Determine
the
follo
wing
probabili-
ties
:
P
X
=
1
;
P
X
=
2
E.7682
1
a
Construct
a
probabilit
y
tree
asso
ciated
with
a
Bernoulli
sc
heme
of
parameter
2
and
0.4
.
b
Note
X
a
random
v
ariable
follo
wing
a
binomial
distri-
bution
of
parameter
2
and
0.4
.
Determine
the
follo
w-
ing
probabilities
:
P
X
=
0
;
P
X
=
1
2
a
Construct
a
probabilit
y
tree
asso
ciated
with
a
Bernoulli
sc
heme
with
parameters
3
and
0.4
.
b
Note
X
a
random
v
ariable
follo
wing
a
binomial
distri-
bution
of
parameter
3
and
0.4
.
Determine
the
follo
w-
ing
probabilities
:
P
X
=
0
;
P
X
=
1
h
ttps:/
/c
hingmath.fr
chapExoCorrec/7670
sacados/7670
E
S
E
S
E
S
E
S
E
S
E
S
E
S
chapExoCorrec/7671
sacados/7671
E
S
E
S
E
S
E
S
E
S
E
S
E
S
chapExoCorrec/7681
sacados/7681
N
N
N
B
N
N
N
N
B
N
N
N
N
B
N
N
N
N
B
B
N
N
N
B
B
N
N
N
N
B
B
N
N
N
N
B
B
N
N
N
N
B
B
B
N
N
N
B
B
B
chapExoCorrec/7682
sacados/7682
1
2
3
4
5
6
7
8
9
10
8.
Binomial
law
and
exp
e
ctation
E.7720
Prop
osition
:
The
exp
ectation
of
a
random
v
ariable
X
fol-
lo
wing
a
binomial
distribution
with
parameters
n
and
p
is
the
n
um
b
er
n
×
p
and
is
denoted
b
y
E
(
X
)
.
In
terpretation
:
The
exp
ectation
is
the
observ
ed
mean
v
alue
of
the
n
um
b
er
of
successes
ac
hiev
ed
in
the
Bernoulli
sc
heme
when
this
random
exp
erimen
t
is
p
erformed
a
large
n
um
b
er
of
times.
1
Consider
a
random
v
ariable
X
follo
wing
the
binomial
dis-
tribution
with
parameters
10
and
0
;
3
.
Determine
the
exp
ectation
of
the
random
v
ariable
X
.
2
Consider
a
random
v
ariable
X
follo
wing
the
binomial
dis-
tribution
with
parameters
24
and
0
;
45
.
Determine
the
exp
ectation
of
the
random
v
ariable
X
.
E.7680
Fiv
e
b
o
ys
and
three
girls
write
their
names
on
a
piece
of
pap
er
and
insert
it
in
to
an
urn.
T
w
o
pieces
of
pap
er
are
dra
wn
successiv
ely
from
the
urn,
with
a
discoun
t.
The
t
w
o
dra
ws
are
considered
to
b
e
indep
enden
t.
1
A
t
eac
h
dra
w,
w
e
lo
ok
to
see
whether
the
pap
er
dra
wn
designates
a
b
o
y
or
a
girl.
Construct
the
probabilit
y
tree
related
to
this
exp
erimen
t.
2
Let
X
b
e
the
random
v
ariable
asso
ciating
with
an
out-
come
of
this
dra
w
the
n
um
b
er
of
girls
selected.
a
Determine
the
probabilit
y
distribution
of
X
.
b
Calculate
its
mathematical
exp
ectation
of
E
(
X
)
.
The
result
will
b
e
rounded
to
the
nearest
thousandth.
E.7685
W
e
ha
v
e
a
w
ell-balanced
cubic
die
whose
faces
are
n
um
b
ered
from
1
to
6
.
When
rolling
the
dice,
the
game
is
considered
w
on
if
an
ev
en
v
alue
is
obtained.
W
e
roll
the
w
ell-balanced
die
three
times
in
succession
and
denote
b
y
X
the
n
um
b
er
of
times
an
ev
en
n
um
b
er
w
as
ob-
tained.
1
Dra
w
up
the
probabilit
y
tree
asso
ciated
with
this
random
exp
erimen
t.
2
Giv
e
the
exact
v
alue,
then
the
v
alue
rounded
to
the
thou-
sandth
of
the
probabilit
y
P
(
X
=
2)
.
3
Giv
e
the
exp
ectation
of
the
random
v
ariable
X
.
9.
Binomial
law
and
r
epr
esentation
E.7686
Belo
w
is
represen
ted
the
la
w
of
the
random
v
ariable
X
follo
wing
the
binomial
la
w
of
parameters
n
=
10
and
p
=
0.3
:
Giv
e
an
appro
ximate
v
alue
for
the
follo
wing
probabilities
:
a
P
X
=
1
b
P
X
=
3
E.7689
Belo
w
is
giv
en
the
represen
tation
of
the
la
w
of
a
random
v
ariable
X
follo
wing
a
binomial
distribution
with
parameter
n
=
10
and
p
=
0.7
.
:
Giv
e
the
inequalit
y
that
is
v
erified
:
a
P
X
<
5
0.5
b
P
X
<
5
0.5
10.
Binomial
law
and
c
alculator
E.7684
Consider
a
random
v
ariable
X
follo
wing
a
binomial
distribution
with
parameters
0.2
and
20
.
Questions
will
b
e
answ
ered
using
the
calculator.
Results
will
b
e
rounded
to
the
nearest
10
−
3
:
1
Determine
the
v
alue
of
the
follo
wing
probabilities
:
a
P
X
=
5
b
P
X
=
9
2
Determine
the
v
alue
of
the
follo
wing
probabilities
:
a
P
X
5
b
P
X
9
E.7807
Consider
a
random
v
ariable
X
follo
wing
a
binomial
distribution
with
parameters
30
and
0.24
.
Questions
will
b
e
answ
ered
using
the
calculator.
Results
will
b
e
rounded
to
the
nearest
10
−
3
:
1
Determine
the
v
alue
of
the
follo
wing
probabilities
:
a
P
X
=
10
b
P
X
=
12
2
Determine
the
v
alue
of
the
follo
wing
probabilities
:
a
P
X
10
b
P
X
18
h
ttps:/
/c
hingmath.fr
chapExoCorrec/7720
sacados/7720
chapExoCorrec/7680
sacados/7680
chapExoCorrec/7685
sacados/7685
chapExoCorrec/7686
sacados/7686
1
2
3
4
5
6
7
8
9
10
chapExoCorrec/7689
sacados/7689
chapExoCorrec/7684
sacados/7684
chapExoCorrec/7807
sacados/7807
E.7687
Consider
a
random
v
ariable
X
follo
wing
the
binomial
distribution
with
parameters
n
=
5
and
p
=
0.63
.
The
probabilit
y
v
alues
will
b
e
rounded
to
three
decimal
places.
1
Determine
the
follo
wing
probabilities
:
a
P
X
=
0
b
P
X
=
1
c
P
X
=
5
2
Giv
e
the
probabilit
y
of
ev
en
t
X
4
.
E.7721
F
or
the
end-of-y
ear
concert,
the
conserv
atory
auditorium
has
400
places
reserv
ed
for
paren
ts.
W
e’re
in
terested
in
the
n
um
b
er
X
of
paren
ts
attending
the
end-of-y
ear
concert
in
the
auditorium.
The
probabilit
y
of
eac
h
500
paren
t
attending
the
concert
is
estimated
at
0.75
.
It
is
assumed
that
X
follo
ws
the
binomial
distribution
with
parameters
500
and
0.75
.
1
Calculate
the
exp
ectation
of
X
.
2
Determine
the
probabilit
y
that
the
n
um
b
er
of
seats
re-
serv
ed
for
paren
ts
is
sufficien
t.
Round
the
result
to
the
thousandth.
E.7688
A
v
accine
is
b
eing
tested
on
a
p
opula-
tion
of
100
individuals.
30
of
them
react
to
this
v
accine
with
high
fev
ers.
Eac
h
test
phase
is
carried
out
on
a
group
of
5
in-
dividuals
c
hosen
at
random
and
indep
enden
tly
b
et
w
een
eac
h
test.
Let
us
note
X
the
random
v
ariable
that
asso
ciates
with
eac
h
test
phase
the
n
um
b
er
of
individuals
who
had
a
reaction
with
high
fev
ers.
1
Justify
that
the
random
v
ariable
X
follo
ws
a
binomial
distribution
with
parameters
5
and
0.3
.
2
Determine
the
probabilit
y
that
2
individuals
reacted
to
the
v
accine
with
fev
er
o
v
er
a
test
phase.
3
Ov
er
a
test
phase,
what
is
the
probabilit
y
that
at
most
4
individuals
ha
v
e
reacted
with
fev
er.
E.7690
By
c
ho
osing
a
pupil
at
random
from
among
those
registered
for
half-b
oard,
w
e
kno
w
that
the
prob-
abilit
y
of
the
c
hosen
pupil
b
eing
satisfied
with
the
half-b
oard
is
0.675
.
W
e
denote
X
the
random
v
ariable
equal
to
the
n
um
b
er
of
stu-
den
ts
declaring
to
b
e
satisfied
with
the
qualit
y
of
the
meals.
As
the
n
um
b
er
of
studen
ts
is
sufficien
tly
large,
w
e
accept
that
X
follo
ws
a
binomial
distribution
with
parameters
4
and
0.675
.
Results
will
b
e
rounded
to
the
thousandth.
1
Calculate
the
probabilit
y
of
the
ev
en
t
A
:
ˇ
no
studen
t
is
satisfait
ı.
2
Calculate
the
probabilit
y
of
the
ev
en
t
B
:
ˇ
all
four
stu-
den
ts
are
satisfied
with
the
qualit
y
of
repas
ı.
11.
Fluctuation
interval
E.7852
A
farmer
sorts
his
tomato
es
according
to
their
size
(c
alibr
e)
.
He
tells
his
suppliers
that
40
%
of
his
tomato
es
are
of
a
calibre
greater
than
or
equal
to
6
(a
diameter
gr
e
ater
than
47
mm
)
.
Visiting
the
farm,
a
supplier
tak
es
30
tomato
es
and
observ
es
that,
among
them,
10
tomato
es
are
of
a
size
greater
than
or
equal
to
6
.
Opp
osite
is
the
cum
ulativ
e
distribution
function
of
a
binomial
random
v
ariable
with
parameters
30
and
0.4
.
The
follo
wing
results
can
b
e
ex-
tracted
from
it
:
P
X
10
≈
0.2915
;
P
X
20
≈
0.9991
1
a
Determine
the
v
alue
of
the
smallest
in
teger
a
that
satisfies
the
condition
:
P
X
a
>
0.025
b
Determine
the
v
alue
of
the
smallest
in
teger
b
that
sat-
isfies
the
condition
:
P
X
b
0.975
c
Deduce
the
fluctuation
in
terv
al
at
the
threshold
of
95
%
of
the
observ
ed
frequency
for
the
random
v
ariable
X
.
(The
limits
wil
l
b
e
r
ounde
d
to
10
−
3
)
2
What
can
b
e
said
ab
out
the
supplier’s
observ
ation?
E.7853
Consider
a
random
v
ariable
X
follo
w-
ing
a
binomial
distribution
with
parameters
30
and
0.32
:
X
∼
B
30
;
0.32
k
0
1
2
3
4
5
6
7
8
P
(
X
k
)
0
0
0.001
0.005
0.018
0.049
0.11
0.208
0.341
k
9
10
11
12
13
14
15
16
17
P
(
X
k
)
0.494
0.645
0.774
0.871
0.934
0.97
0.988
0.995
0.999
k
18
19
20
21
22
23
24
25
26
27
28
29
30
P
(
X
k
)
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Determine
the
smallest
in
tegers
a
and
b
suc
h
that
:
P
X
a
)
>
0.025
;
P
X
b
0.975
2
Justify
that
:
P
a
X
b
0.95
3
Let
F
=
X
30
b
e
the
random
v
ariable
represen
ting
the
ran-
dom
frequency
of
success.
Justify
that
:
P
a
30
F
b
30
0.95
12.
Unclassifie
d
financial
ye
ars
h
ttps:/
/c
hingmath.fr
chapExoCorrec/7687
sacados/7687
chapExoCorrec/7721
sacados/7721
chapExoCorrec/7688
sacados/7688
chapExoCorrec/7690
sacados/7690
chapExoCorrec/7852
sacados/7852
chapExoCorrec/7853
sacados/7853
E.11859
L’exercice
n’existe
pas.
h
ttps:/
/c
hingmath.fr
sacados/11859
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