Grade 11 - STMG
/ conditional probability 18 exercises (including 16 corrected)
- Probability tree construction (6 exercices)
- Conditional Probability: Introduction (2 exercices)
- Conditional probability (1 exercice)
- Independent events (8 exercices)
CTRRCTRR
MMEMME
E.11538
A
game
consists
of
shaking
and
turning
a
bottle
upside
down
to
remove
one
of
its
contents.
Here
is
the
content
of
this
bottle:
We
assume
that
the
law
of
equiprobability
applies
to
this
ran-dom
experiment.
We
consider
the
4
events
below
:
R
:
ˇ
The
item
that
comes
out
is
a
stripe
ı
;
C
:
ˇ
The
item
that
comes
out
is
a
square
ı
;
T
:
ˇ
The
item
drawn
is
a
triangle
ı
;
R
:
ˇ
The
item
drawn
is
a
circle
ı
;
Construct
the
probability
tree
:
E.11539
A
toy
company
specializes
in
manufacturing
dolls
that
talk
and
walk.
Each
doll
can
have
two
defects
and
only
two:
one
mechanical
defect
and
one
electrical
defect.
A
statistical
study
shows
that
:
8%
of
the
dolls
have
the
mechanical
defect
;
5%
of
the
dolls
have
the
electrical
defect
;
2%
of
the
dolls
have
both
defects.
Daily
production
is
1,000
dolls.
1
Copy
and
complete
the
table
below,
which
describes
daily
production
:
dolls
with
mechanical
defect
Dolls
without
mechanical
defect
total
Dolls
with
electrical
defect
Dolls
without
electrical
defects
Total
80
1
000
In
the
rest
of
the
exercise,
each
numerical
result
will
be
given
in
decimal
form.
2
A
doll
is
randomly
selected
from
the
day’s
production.
Consider
the
two
events
below
:
E
:
"
the
doll
selected
has
an
electrical
defect
"
M
:
"
The
sampled
doll
has
a
mechanical
defect
"
3
a
Determine
the
probability
of
event
E
and
event
E
b
Assuming
that
the
doll
selected
has
an
electrical
defect,
what
is
the
probability
that
this
doll
has
a
mechanical
problem?
c
Assuming
that
the
doll
selected
does
not
have
an
elec-trical
defect,
what
is
the
probability
that
this
doll
has
a
mechanical
problem?
4
Complete
the
probability
tree
below
:
https://chingmath.fr
chapExoCorrec/11538
sacados/11538
CTRRCTRR
chapExoCorrec/11539
sacados/11539
MMEMME
Demi-pensionnaireGarçon
AB
E.11540
In
a
high
school
with
2000
students,
the
distribution
of
stu-dents
by
gender
and
choice
of
first
foreign
language
is
given
as
follows
1
A
student
claims
"
that
there
are
as
many
girls
as
boys
in
this
high
school"
.
Is
he
right?
Justify
your
answer.
A
student
is
chosen
at
random,
with
equal
probability,
from
this
high
school.
Consider
the
following
events
:
Girls
Boys
English
712
728
Other
LV1
288
272
F
:
"thestudent
is
a
girl";
A
:
"thestudent
has
chosen
English
as
their
first
foreign
language"
In
the
following
questions,
the
results
will
be
given
as
frac-tions
that
do
not
need
to
be
simplified.
2
Determine
the
probability
of
event
A
∩
F
.
3
Determine
the
probability
of
event
A
given
that
event
F
has
occurred.
4
Are
events
A
and
F
independent?
Justify
your
answer.
5
We
know
that
the
chosen
student
is
a
boy.
Consider
the
following
statement
:
"
The
probability
that
he
chose
English
as
his
first
foreign
language
is
more
than
three
times
greater
than
the
prob-ability
that
he
did
not
choose
English
as
his
first
foreign
language.
".
Is
this
statement
true?
Justify
your
answer.
E.11541
We
have
a
biased
coin
for
which
the
probability
of
getting
heads
when
tossed
is
equal
to
1
4
.
1
Determine
the
probability
of
getting
tails.
2
We
flip
this
coin
three
times
in
a
row,
with
each
flip
be-ing
independent,
and
note
the
result
(heads
or
tails)
for
each
flip.
a
Represent
the
situation
using
a
probability
tree.
b
What
is
the
probability
of
getting
heads
exactly
once
in
these
three
tosses?
c
What
is
the
probability
of
never
getting
heads?
2.
Conditional
Probability:
Introduction
E.11511
In
a
statistical
study,
we
con-sider
a
class
of
24
students,
where
each
student
is
repre-sented
by
a
box
in
the
graph
be-low
:
G
:
ˇ
the
student
is
a
boy
ı
;
D
:
ˇ
the
student
is
a
day
boarder
ı.
The
random
experiment
con-sists
of
choosing
a
student
at
random
from
the
class
and
see-ing
whether
or
not
these
two
cri-teria
are
met
:
1
a
Determine
the
probability
of
choosing
a
"
boy
".
b
Knowing
that
a
"
boy
"has
been
chosen,
what
is
the
probability
of
choosing
a
"
day
student
"
c
Determine
the
probability
of
choosing
a
"
boy
"who
is
a
"
day
student
".
d
What
do
we
notice?
2
a
Determine
the
probability
of
choosing
a
"
girl
".
b
Given
that
a
"
girl
"has
been
chosen,
what
is
the
prob-ability
of
choosing
a
"
day
student
"
c
Determine
the
probability
of
choosing
a
"
girl
"who
is
"
a
day
student
".
d
What
do
we
notice?
E.11513
Consider
the
universe
Ω
and
its
two
events
A
and
B
are
rep-resented
:
Use
the
law
of
equiprobability.
1
a
Determine
the
probability
of
event
A
.
b
Knowing
that
event
A
has
occurred,
determine
the
probability
of
event
B
.
c
Determine
the
probability
of
event
A
∩
B
.
d
What
do
we
notice?
2
a
Determine
the
probability
of
event
A
.
b
Knowing
that
event
A
has
occurred,
determine
the
probability
of
event
B
.
c
Determine
the
probability
of
event
A
∩
B
.
d
What
do
we
notice?
3.
Conditional
probability
E.11512
In
a
statistical
study,
we
consider
a
class
of
24
students,
where
each
student
is
represented
by
a
box
in
the
graph
below
:
https://chingmath.fr
chapExoCorrec/11540
sacados/11540
chapExoCorrec/11541
sacados/11541
chapExoCorrec/11511
sacados/11511
Demi-pensionnaireGarçon
sacados/11513
AB
chapExoCorrec/11512
sacados/11512
ClasseBDemi-pensionnaireGarçon
::::::G:::GD::::::G:::GD
AB
CD
0112101102011112
BBABBA
0;20;41B0;59BA0;80;41B0;59BA
Two
characteristics
are
studied
in
the
individuals
in
this
study
:
G
:
ˇ
the
student
is
a
boy
ı
;
D
:
ˇ
the
student
is
a
day
student
ı.
The
random
experiment
consists
of
choosing
a
student
at
ran-
dom
from
the
class
and
seeing
whether
or
not
these
two
cri-teria
are
met.
1
a
Determine
the
probability
of
choosing
a
"
boy
".
b
Knowing
that
a
"
boy
"has
been
chosen,
what
is
the
probability
of
choosing
a
"
day
student
"
c
Determine
the
probability
of
choosing
a
"
boy
"who
is
"
an
external
student
".
d
What
do
we
notice?
2
a
Determine
the
probability
of
choosing
a
"
girl
".
b
Given
that
a
"
girl
"has
been
chosen,
what
is
the
prob-ability
of
choosing
an
"
external
student
"
c
Determine
the
probability
of
choosing
a
"
girl
"who
is
"
external
".
d
What
do
we
notice?
4.
Independent
events
E.11591
Consider
the
random
experiment
of
universe
Ω
represented
below
and
provided
with
the
law
of
equiprobability:
1
Consider
the
two
events
A
and
B
shown
below
:
Determine
the
following
probabilities
:
a
P
A
B
b
P
B
2
Consider
the
two
events
C
and
D
shown
below
:
Determine
the
following
probabilities
:
a
P
C
D
b
P
D
Definition:
let
A
and
B
be
two
events.
The
events
A
and
B
are
said
to
be
independent
P
A
B
=
P
B
.
3
Are
(
A
;
B
)
and
(
C
;
D
)
pairs
of
independent
events.
E.11592
Un
The
game
consists
of
spinning
the
wheel
opposite
once
and
not-ing
the
color
of
the
square
ob-tained,
then
spinning
the
wheel
a
second
time
and
noting
the
num-ber
obtained.
The
two
throws
of
the
wheel
are
obviously
independent
of
each
other.
Consider
the
two
events
:
A
:
ˇ
the
box
obtained
is
grey
on
the
first
tirage
ı
;
B
:
ˇ
the
resulting
square
is
numbered
0
on
the
second
tirage
ı.
1
a
Determine
the
probabilities
:
P
B
;
P
A
B
b
Are
the
events
A
and
B
independent?
2
Complete
the
probability
tree
:
E.11593
In
a
random
experiment,
consider
two
events
A
and
B
allowing
the
probability
tree
to
be
con-structed
:
1
Determine
the
probability
of
the
event
B
.
2
Establish
that
the
events
A
and
B
are
independent.
https://chingmath.fr
ClasseBDemi-pensionnaireGarçon
::::::G:::GD::::::G:::GD
chapExoCorrec/11591
sacados/11591
AB
CD
chapExoCorrec/11592
sacados/11592
0112101102011112
BBABBA
chapExoCorrec/11593
sacados/11593
0;20;41B0;59BA0;80;41B0;59BA
NombredebulbesdetulipejauneNombredebulbesdetuliperougeNombredebulbesdetulipenoireTotalNombredebulbesdetulipequiπeurirontNombredebulbesdetulipequineπeurirontpasTotal1000
E.11594
In
a
class
of
30
students,
there
is
a
drawing
club
and
a
theater
club.
The
drawing
club
has
10
members,
and
the
theater
club
has
6
members.
Two
students
are
members
of
both
clubs.
A
student
from
the
class
is
chosen
at
random
and
asked
a
question.
We
call:
D
the
event
:
ˇ
The
student
is
a
member
of
the
drawing
club
ı
;
T
the
event
:
ˇ
The
student
is
a
member
of
the
theater
club
ı.
Show
that
events
D
and
T
are
independent.
E.11595
A
gardener
has
a
bag
filled
with
1.000
tulip
bulbs.
These
include
:
60
%
are
yellow
tulip
bulbs
;
25
%
are
red
tulip
bulbs
;
the
rest
are
black
tulip
bulbs.
In
addition
:
28
%
of
all
these
bulbs
will
not
flower;
80
%
of
the
yellow
tulip
bulbs
will
flower;
60
black
tulip
bulbs
will
not
flower.
Part
A
Copy
and
complete
the
table
below
:
Part
B
The
gardener
draws
a
bulb
at
random
from
his
bag.
We
note
:
F
the
event
:
ˇ
The
bulb
will
bloom
ı
;
J
:
ˇ
The
bulb
is
that
of
a
tulip
jaune
ı
;
R
:
ˇ
The
bulb
is
that
of
a
tulip
rouge
ı
;
N
:
ˇ
The
bulb
is
that
of
a
tulip
noire
ı.
1
Determine
the
probabilities
of
the
following
events
:
J
∩
F
,
J
,
F
,
J
∪
F
.
2
Are
the
events
J
and
F
independent?
Justify
the
answer.
E.11596
During
the
manufacture
of
a
pair
of
spectacles,
the
pair
of
lenses
must
undergo
two
treatments
noted
T
1
and
T
2
.
One
pair
of
glasses
is
taken
at
random
from
the
production.
We
denote
by
A
the
event
:
ˇ
the
pair
of
lenses
has
a
defect
for
the
T
1
treatment.
We
denote
by
B
the
event
:
ˇ
the
pair
of
glasses
has
a
defect
for
treatment
T
2
ı.
We
note
A
and
B
respectively
the
opposite
events
of
A
and
B
.
One
study
showed
that
:
the
probability
that
a
pair
of
lenses
has
a
defect
for
T
1
noted
P
A
is
equal
to
0.1
.
the
probability
that
a
pair
of
lenses
has
a
defect
for
T
2
noted
P
B
is
equal
to
0.2
.
the
probability
that
a
pair
of
lenses
has
neither
defect
is
0.75
.
1
Copy
and
complete
the
following
table
with
the
corre-sponding
probabilities.
A
A
Total
B
B
Total
1
2
a
Determine,
justifying
the
answer,
the
probability
that
a
pair
of
lenses,
taken
at
random
from
production,
will
have
a
defect
for
at
least
one
of
the
two
treatments
T
1
or
T
2
.
b
Give
the
probability
that
a
pair
of
lenses,
taken
at
ran-dom
from
production,
has
two
defects,
one
for
each
T
1
treatment
and
T
2
.
c
Are
the
events
A
and
B
independent?
Justify
the
an-swer.
https://chingmath.fr
chapExoCorrec/11594
sacados/11594
chapExoCorrec/11595
sacados/11595
NombredebulbesdetulipejauneNombredebulbesdetuliperougeNombredebulbesdetulipenoireTotalNombredebulbesdetulipequiπeurirontNombredebulbesdetulipequineπeurirontpasTotal1000
chapExoCorrec/11596
sacados/11596
Demi-pensionnaireGarçon
E.11485
In
a
statistical
study,
we
con-sider
a
class
of
24
students,
where
each
student
is
repre-sented
by
a
box
in
the
graph
be-low
:
G
:
ˇ
the
student
is
a
boy
ı
;
D
:
ˇ
the
student
is
a
day
boarder
ı.
The
random
experiment
con-sists
of
choosing
a
student
at
random
from
the
class
and
see-ing
whether
or
not
these
two
cri-teria
are
met
:
1
a
Determine
the
probability
of
choosing
a
"
boy
".
b
Knowing
that
a
"
boy
"has
been
chosen,
what
is
the
probability
of
choosing
a
"
day
student
"
c
Determine
the
probability
of
choosing
a
"
boy
"who
is
a
"
day
student
".
d
What
do
we
notice?
2
a
Determine
the
probability
of
choosing
a
"
girl
".
b
Given
that
a
"
girl
"has
been
chosen,
what
is
the
prob-ability
of
choosing
a
"
day
student
"
c
Determine
the
probability
of
choosing
a
"
girl
"who
is
"
a
day
student
".
d
What
do
we
notice?
E.11620
Une
entreprise
ferme
aux
mois
de
juil-let
et
août.
L’ensemble
des
180
employés
d’une
entreprise
prennent
leurs
congés
pendant
cette
période.
On
a
les
informations
suivantes
:
28
hommes
ont
pris
leurs
vacances
en
juillet.
138
personnes
ont
pris
leurs
vacances
en
août.
L’entreprise
compte
60
femmes.
On
crée
une
expérience
aléatoire
en
choisissant
au
hasard
un
employé
de
cette
entreprise.
On
considère
les
deux
événements
ci-dessous
:
F
:
"l’employé
choisi
est
une
femme
";
J
:
"l’employé
choisi
prend
ses
vacances
en
juillet
".
1
Reproduire
et
compléter
le
tableau
ci-contre
:
Juillet
Août
Total
Femmes
en
vacances
Hommes
en
vacances
Total
en
vacances
2
Donner
les
probabilités
:
P
(
F
)
;
P
(
F
∩
J
)
;
P
(
P
(
F
∩
J
)
3
a
Déterminer
la
probabilité
P
J
(
F
)
.
b
Est-ce
que
les
événements
F
et
J
sont
indépendants
?
Justifier.
5.
Shares
E.11584
Un
village
propose
aux
partici-pants
de
la
fête
du
sport
deux
épreuves
:
une
randonnée
et
un
cross.
Il
n’est
pas
possible
de
s’inscrire
aux
deux
épreuves
à
la
fois.
On
dispose
des
informations
suivantes
:
90%
des
participants
ont
choisi
la
randonnée,
parmi
eux,
5%
sont
licenciés
dans
un
club.
10%
des
participants
ont
choisi
le
cross,
parmi
eux,
40%
sont
licenciés
dans
un
club.
Un
journaliste
interroge
un
participant
au
hasard.
On
considère
les
événements
suivants
:
R
:
"
Le
participant
a
choisi
la
randonnée
"
L
:
"
Le
participant
est
licencié
dans
un
club
"
1
Par
simple
lecture
de
l’énoncé,
indiquer
:
a
La
probabilité
que
le
participant
interrogé
soit
licencié
dans
un
club
sachant
qu’il
a
choisi
la
randonnée.
b
La
probabilité
que
le
participant
interrogé
soit
licencié
dans
un
club
sachant
qu’il
a
choisi
le
cross.
En
prenant
connaissance
de
ces
deux
probabilités,
le
journaliste
estime
que
s’il
choisit
un
participant
parmi
ceux
qui
sont
licenciés
dans
un
club,
la
probabilité
qu’il
ait
effectué
le
cross
sera
largement
supérieure
à
50%.
L’objectif
des
questions
suivantes
est
de
vérifier
si
cette
intuition
est
correcte.
2
Représenter
la
situation
par
un
arbre
de
probabilités.
3
a
Déterminer
la
probabilité
que
le
participant
inter-rogé
ait
choisi
le
cross
et
soit
licencié
dans
un
club.
b
Vérifier
que
la
probabilité
que
le
participant
interrogé
soit
licencié
dans
un
club
est
égale
à
850
10
000
;
soit
8
;
5%.
4
Le
journaliste
interroge
un
participant
licencié
dans
un
club.
Déterminer
la
probabilité
que
ce
participant
ait
choisi
le
cross.
L’intuition
du
journaliste
est-elle
correcte
?
https://chingmath.fr
chapExoCorrec/11485
sacados/11485
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chapExoCorrec/11620
sacados/11620
sacados/11584