Peluang suatu kejadian kelompok 7

Pe l u a n g s u a t u
k e j a d i a n
• Pe r c o b a a n :
p e r c o b a a n
a d a l a h
s u a t u
t i n d a k a n
a t a u
k e g i a t a n
y a n g
d a p a t
me mb e r i k a n
• R u a n g aS aam p e l : n g k i n a n h a s i l
b e b e r
p
k mu
r u a n g s a mp e l a d a l a h
h i mp u n a n s e mu a h a s i l y a n g
mu n g k i n d a r i
p K e jc a d ia a n :
o b a n
• e r

s u a t u

K e j a d i a n (e v e n t ) a d a l a h
s a l a h s a t u s u b h i mp u n a n
(s u b s e t ) A d a r i r u a n g s a m p e l
S

Contoh:
s e
d i
d a
s e
d i
s e
mn
R u ae
y a

p
b
n
b
a
c
n
g
n

u l u h k a r t u i d e n t i k
e r i n o m o r 0, 1, 2, 3,…, 9
d i t e mp a t k a n d a l a m
u a h k o t a k t e r t u t u p
mb i l s a t u k a r t u
a r a a c a k d a n
g m p 0al 2 Si = n o ,8 9
k a r t u
s aa me,1, t ,3, 4 ,5 , 6 , 7m,o , r
g t e r a mb i l .

A n g k a -a n g k a 0,1,2,3, …, 9 a d a l a h a n g k a -a n g k a
y a n g mu n g k i n t e r p i l i h d a l a m p e r c o b a a n
d i
a t a s
d i s e b u t
t i t i k
s a mp e l
a t a u
g
p u n a n
a S eg m bo at r a a rn u a hn i g ms a m p e l b a g i a n d a l a m
n g
r u a n g s a mp e l d i n a ma k a n k e j a d i a n a t a u
1,3 ,5 , 7 ,9
e v e n t (E ), m i s a l E =
a d a l a h
k e j a d i a n k a r t u y a n g
t e r a mb i l

b e r n o mo r

g a n j i l

T e o r e ma
J i
t e
t i
s e
ma
p e
a d
d i
ma

k
r
t
r
s
l
a
h
k

a
d
i
u
i
u
l
a
a

r u a n g
s a mp e l
S
i r i
d a r i
t i t i k k
s a mp e l
y a n g
p a s e h i n g g a ma s i n g n g
m e m p u n n (a i )
y E
a n g y a n g s P ( E ) d ann S E
a ma
( )
a h
k e j a d i a n
y a n g
r a p k a n
t e r j a d i
:

d e n g a n n (E ): b a n y a k
a n g g o t a E

Contoh:
•Pe r c o b a a n
p e n g a mb i l a n s e b u a h
k a r t u s e c a r a a c a k
d a r i k ao at l a h kk e jba e i ra ni s i 10
a
d
d
E1
1
k ea a p t pue l t iue arda gm b n lr tak m br ikl u k a r t u
r a
e t ie
ia t
B r
n o mo r 1
b e r n
b e r m r m
bSee rt ni oa n o o a 1? t o r d e0,t i1, ,2, h3,n …, 9.
p k r
u i
n
k s e i
g g a
s e t i a p k a r t u me n d a p a t
s a ma u n t u k t e r p i l i h .
Ba n y a k a n g g o t a E

1

p e l u a n g y a n g

a t a u n (E 1)= 1

1
B a n y a k a n g g o t a r u a n g s a m p e l n ( E(S ) = 10
n 1)
P ( E1 )
P e l u a n g t e r a mb i l
n(S )
10
k a r t u b e r n o mo r 1
a d a l a h :

Contoh:
• P e r c o b a a n p e n g a mb i l a n
s e b u a h k a r t u s e c a r a
a c a k d a r i k o t a k b e r i s i 10
k a r t u i d e n t i k b e r n o mo r
E2
1,3,5 , 7 ,9 a d a l a h k e j a d i a n
0, 1, 2, 3, …, 9. t e r a m b i l k a r t u
Be r
b eS
r
s
y
B
B
P
n
k
a

b e r n o mo r g a n j i l
a p a p e l u a n g t e r a mb i l k a r t u
n
o r g a n i
e to im a p k a r tj u l i ?d e n t i k , s e h i n g g a
e t i a p k a r t u me n d a p a t p e l u a n g
a n g s a ma u n t u k t e r p i l i h .
a n y a k a n g g o t a E 2 a t a u n (E 2)= 5
a n y a k a n g g o t a r u a n g s a mp e l
n(E 2 )
e l )u=a 10 g t e r a m b i l
n
(S
P(E2 )
n(S )
a r t u b e r n o mo r g a n j i l
d a l a h :

5

1

10

2

Contoh:
0,
E 1, 02,23, 4…, ,9. ,9
,1, ,3 , ,5 , 6 7 ,8
3

a d a l a h k e j a d i a n t e r a mb i l
b e r n o m o r 0,1,2,3,…, a t a u 9

k a r t u

Berapa peluang terambil kartu bernomor 0, 1,2,3, …,9?
Se t
k a r
u n t
Ba n
Ba n
Pe l
k a r

i a p k a
t u me n
u k t e r
y a k a n
y a k a n
u a n g t
t u b e r

r t u i d e n t i k , s e h i n g g a s e t i a p
d a p a t p e l u a n g y a n g s a ma
p i l i h .
g g o t a E 3 a t a u n (E 3)= 10
g g o t a r u a n g s a m p e l n (S () = 10
n E3 )
10
P (E3 )
1
e r a mb i l
n(S )
10
n o mo r g a n j i l

Contoh:
E4
0, 1, 2, 3, …, 9.
a d a l a h k e j a d i a n t e r a mb i l
b e r n o mo r
10

k a r t u

Berapa peluang terambil kartu bernomor 10?
Se t
k a r
u n t
Ba n
Ba n
Pe l
k a r

i a p k a
t u me n
u k t e r
y a k a n
y a k a n
u a n g t
t u b e r

r t u i d e n
d a p a t p e
p i l i h .
g g o t a E4
g g o t a r u
e r a mb i l
n o m o r 10

t i k , s e h i n g g a s e t i a p
l u a n g y a n g s a ma
a t a u n (E 4)= 0
a n g s a m p e l n n ( E 4 )= 100
(S )
P(E4 )
n(S )
10

0

Ki s a r a n n i l a i
p e l u a n g s u a t u
k e j a d i a n
Mi s a l k a
r u a n g s a
a d a l a h k
Karena E
S dari
y a n g d i h
tsehingga a n ( i )
e r j
d

n S a d a l a h
mp e l d a n E
e j a d i a n
E , maka
E
a r a p k a n
n( E )

n(S )

n( )

n(E )

n(S )

n(S )

n(S )

n(S )

0
P (E ) = 0,
k e j a d i
(E j a d
t Pe r ) = 1,
k e j a d i

P(E )

1

ma k a k e j a d i a n E d i
a n y a n g t i d a k mu n g
im a k a k e j a d i a n E d i
a n y a n g p a s t i t e r j

s e b u t
k i n
s e b u t
a d i

S

Contoh:
1. S e b u a h d a d u d i l e m p a r
s e k a l i .
Te n t u k a n :
a . r u a n g s a mp e l
p e r c o b a a n t e r s e b u t
d a n
j u ml a h a n g g o t a
r u a n g s a mp e l .
b . p e l u a n g mu n c u l
ma t a d a d u g a n j i l

P e mb a h a s a n :
a .R u a n g s a m p e l 1, 2 , 3, 4 ,5 , 6 ,
S
J u ml a h a n g g o t a
n(S )
6
r u a n g s a mp e l
b . mi s a l E 1 a d a l a h k e j a d i a n
m u n c u l m a t a d a d u g a n j i l n(E )
E1

1,3 ,5

n ( E1 )

J a d i p e l u a n g
ma t a d a d u g a n
c a M ia s a lh E 2 a d a l
. d l a
mu n c u l ma t a d a
n(E2 )
4 E 2 1, 2 ,3

3

mu
j i
a h
d u
3

3

1

6

2

1
n c u l
2
l
k e j a d i a n
k u r a n g nd E )r i 3
( a
2

1

P ( E1 )

P(E2 )

1

n(S )

n(S )

6

J a d i p e l u a n g mu n c u l ma t a
1
d a d u k u r a n g d a r i 4 a d a l a h : 2

2

Contoh:
1. D u
d i
s a
Te
a
s i
b
g a

a
u a n g
l o g a m
l e mp a r
b e r s a ma ma
s a t u
k a l i .
n t u k a n p e l u a n g :
. mu n c u l n y a s a t u
s i g a mb a r
. mu n c u l n y a d u a
mb a r

Pembahasan:
• R u a n g s a mSp e( A , A ), ( A , G ), (( G , A ), ( G , G )
l
n(S )

4

a . Mi s a l E 1 a d a l a h k e j a d i a n
mu n c u l n y a s a t u s i s i g a mb a r
E1

n ( E1 )

( A , G ), (( G , A )
n( E1 )

2

1

J a d i
n(S )
4
2
mu n c
s a t u
b . Mi s a l E 2 a d g a mb
a l a h
a d a l
mu n c u l d u a g a mb a
P ( E1 )

E2

(G , G )

n(E 2 )

1

2

p e l u a n g
1
u l
2
s i s i
akr e j a d i a n
ra h
n(E )
P(E2 )

2

n(S )

J a d i p e l u a n g mu n c u l
d u a s i s i g a mb a r a d a l a h

1
4

1
4

So a l :
Da r i d a l a m s e b u a h k o t a k
t e r d a p a t
4
k e l e r e n g
me r a h , 3 k e l e r e n g
b i r u ,
d a n
2
k e l e r e n g
h i j a u
d i a mb i l
s e c a r a
a c a k
3
k e l e r e n g
s e k a l i g u s .
Ta e n t e l k ear n n g m e r a h dpa e l 1 u a n g
. 2 k u
e
n
kk e ll e rr e nng g b i y a n g
e
t e r a mb i l
e e
r u
. 1 d
g i
t b e r k ei l r e ir edn a r m e :r a h , 1 k e l e r e n g
b i r u , d a n 1 k e l e r e n g h i j a u
c . Ke t i g a n y a b e r wa r n a
me r a h

J a wa b :
a .
Ba n y a k
k e l
s e l u r u h n y a a d a 9
• Ba n y a k
c a r a
p! e n g a m b i
9
C3
84
9 s e k a l
k e l e r e n g
i g u s
6!3!
d a l d a m j u m l k o t as ke m e s t a
a
J a i
a h
.p e n g a m b i l a n
t i g a
n(S )
84
s e mb i l a n k e l e r e n g a d a
• a d a
4
k e l e r e n g
s e h i n g g a
b a n y a k
p e n g! a m b i l a n 2 k e l e r e n g
4
C2 r i
4
d a 2!2! d6 a l a m k o t a k a d a

e r e n g

l a n
3
d a r i
d a la a h
p d a
d a r i
l a h
me r a h
c a r a
me r a h

s e d a n g k a n b a n y a k c a r a
p e n g 3! m b i l a n 1 k e l e r e n g b i r u
a
3 d
a C 1a l 2a !h 3
!
1

J a w a b (l a n j u t a n )
• B
k
k
s

a
e
e
e

n
l
l
h

y
e
e
i

a
r
r
n

k c a r a p e n g
e n g m e r a hC d
C2 3 1
4
e n g b i r u a d
g 18 a 3
g
84

a mb i l a n 2
a
1
6 . 3n 18
a l a h

14

b. D ePn(2m ,1b ) a r a y a n g s a m a p e l u a n g
g a n c =
t e r a mb i l 1 k e l e r e n g me r a h , 1
k e l e r e n g b i r u d a n 1 k e l e r e n g
C
P (1m ,1b , 1h ) 4 = 1 3 C 1 2 C 1 4 . 3 . 2 2
h i j a u a d a l a h :
9

C3

84

7

c. P e l u a n g t e r a m b i l k e t i g a
k e l e r eC g 4 e r s e b u t me r a h
n
t
1
aPd(3m ) = C
a l a h :
84
21
4

3

9

3

Fr e k u e n s i
h a r a p a n

• Fr e k u e n s i
h a r a p a
s u a t u
k e j a d i a n
p a d
p e r c o b a a n
y a n
d i l a k u k a n N k a l i a d a l a
h a s i l
k a l F i ( E ) N p (e )l u a n
P E
h
k e j a d i a n
t e r s e b u
d e n g a n
b a n y a k n y
C
p eor n to o a a n .
c b h :
d
u d
k
:
D ui ar d am uu s d i al n m pe b abge a is a m a
e s a r
r
s e
f r
mu
b e

b
e
n
r

a
k
c
j

n
u
u
u

y a
e n
l n
ml

n
a
g
h
g
t
a

a
k
36 k a l i . T e n t u k a
s i
h a r a p a
y a
ma t a
d a d
a h 11 a t a u 12

n
n
n
u

Co n t o h :
Du
s e
f r
ma

a
d a d u
d i l e mp a r
b e
b a n y a k
36
k a l i .
T
e k u e n s i
h a r a p a n
mu
t a d a d u b e r j u m l a h 11 a

r
e
n
t

s
n
c
a

a
t
u
u

ma a n
u k a n
l n y a
12

• J a wa b :
Mi s a l k a n
E
a d a l a h
k e j a d i a n
m u n( 5c6 ), ( 6l,6 ), ( 6 ,6 ) ;j nuE m l 3 a h
E
, u
( )
m a t a d a d u 11 a t a u 12, m a k a
P(E )

n(E )

3

1

n(S )

36

12

, Fh

N

P(E )

36

1
12

3 kali

Ke j a d i a n
Ma j e mu k
K o mp l e me n
k e j a d i a n
E
d i
Ec
a d a l a h
k e j
Co n t o h :
t i d a k t e r j a d i n
Mi
me
d e
n
S o
d a

E

c

c

a t u
l i s
i a n
E

s a l k a n
p a d a
p e r c o b a a
n g a mb i l
s a t u
k a r t u
d a r
l a p a n
k a r t u
y a n g
d i b e r
mo ,
1,2,3,4,5,6,7,d a n
8
d a r
1, 2 ,3r4 ,5 , 6 , 7 ,8
l a m s e b u a h k o t a k

jika E

E

s u
t u
a d
y a

1, 2 ,3 adalah kejadian t erambil kartu bernomor

: Ke j a d i a n t i d a k
t e r a mb i l k a r t u <
4 4 , 5 , 6 , 7 ,8

4

n
i
i
i

c

H u b u n g a n a P ( t ) dana P ( E )
n Ea r
P(E )

n(E )

c

P(E )

n(S

n(S )

c

P(E )

1

P(E )

8

n(S )

n(S )

n(S )

P(E )

Pa d a p e r c o b a a n d i

3

E)

dan

a t a s

P(E

c

)

5
8

1

So a l :
Se b u a h k o t a k b e r i s i
b o l a
me r a h ,
3
b o l
p u t i h ,
d a n
2
b o l
k u n i n g .
Te n t u k a
J a wa b :
p e l u a n g t e r a mb i l
b o l
S eb u k u h n y a n d a g k e l e r e n g
l u r a n k u a i n 10
n (s )=10

Mi s a l K a
t e r a mb i l
k e l e r e n g
n (K )= 2
c
K : kejadian t

d a l a h k e j a d i a n
k e l e r e P ( K ) k n ( K )i n 2g , 1
n g
u n
k u n i n g a d a n2, ) m a k a 5
(S
10

erambil kelereng
P(K

bukan kuning
C

)

1

P(K )

4
5

5
a
a
n
a

Ke j a d i a n
ma j e mu k
• Mi
a d
p a
s a
P ( E1

P ( E1

s a l k a n E1 d a n E2
a l a h d u a k e j a d i a n
d a p e r c o b a a n y a n g
m a n:( E E ) n ( E ) n ( E ) n ( E E )

E2 )

E2 )

1

2

1

n(S )

P ( E1 )

2

1

2

n(S )

P(E2 )

P ( E1

E 2 ) …(1
)

Du a k e j a d i a n
s a l i n g l e p a s
• Du
s a
a s
me
k1e
E
d
P ( Ea
s e
1

a
l i
i n
r u
jE 2 a
p a
E )
c a
2

k e j a d i a n
y
n g l e p a s (s a l
g :d i s j o i n t )
p a k a n
d i a n y a n g t i
t n(E E ) 0
t e r j
)
r an ( Sb e r s a m a a n
1

2

a n g
i n g
d u a
d a k
a d i

S e h i n g g a (1) mP ( E 1 j E 2 )d iP (:E 1 ) P ( E 2 )
e n a

Du a k e j a d i a n
s a l i n g b e b a s
• Du
s a
a r
y a
me
k e
• Du
s a
d a

a k e j a d i a n y a n g
l i n g b e b a s
t i n y a k e j a d i a n
n g s a t u t i d a k
mp e n g a r u h i
P ( E1
E 2 ) P ( E1 ) P ( E 2 )
j a d i a n y a n g l a i n
a k e j a d i a n E1 d a n E2
l i n g b e b a s j i k a
n h a n y a j i k a

L a t i h a n
1. S e b u a h
s a t u k a l
p e l u a n g
d a d u b i l

d a d u d i l e mp a r
i . Be r a p a b e s a r
mu n c u l n y a ma t a
a n g a n p r i ma ?

2. D a r i s e p e r a n g k a t k a r t u
b r i d g e d i a mb i l s e b u a h
k a r t u s e c a r a a c a k .
Be r a p a k a h p e l u a n g
k e l u a r n y a k a r t u As ?

3. D a l a m s e b u a h k o t a k
t e r d a p a t 10 b o l a y a n g

4. P e l u a n g s e o r a n g a n a k t e r k e n a
s u a t u p e n y a k i t a d a l a h 0,15 .
J u m l a h a n a k d a r i 1000 a n a k y a n g
d i p e r k i r a k a n t i d a k t e r k e n a
p e n y a k i t i t u a d a l a h …
5. T i g a k e p i n g m a t a u a n g l o g a m
y a n g s a ma d i l e mp a r b e r s a ma s a m a s e b a n y a k 40 k a l i . F r e k u e n s i
h a r a p a n a g a r mu n c u l n y a 2 g a mb a r
d i s e b e l a h a t a s a d a l a h ...

P e mb a h a s a n

1. M i s a l k a n k e j a d i a n m u n c u l n y a
ma t a d a d u b i l a n g a n p r i ma
d i s i mb o l k a n d e n g a n A , ma k a A =
{2, 3, 5} d e n g a n r u a n g s a m p e l n y a
a d a l a h S = {1, 2, 3, 4, 5, 6}. S e h i n g g a
n (A ) = 3 d a n n (S ) = 6. D i p e r o l e h
p e l u a n g mu n c u l n y a ma t a d a d u
b i l a n g a n p r i m a a d a l a h P (A ) = 3/6
= 1/2.
2. M i s a l k a n k e j a d i a n k e l u a r n y a
k a r t u A s d i s i mb o l k a n d e n g a n
B , m a k a n (B ) = 4 d a n n (S ) = 52.
S e h i n g g a , P (B ) = 4/52 = 1/13. J a d i
p e l u a n g mu n c u l n y a k a r t u A s
a d a l a h 1/13.
3. M i s a l k a n C a d a l a h k e j a d i a n
t e r a mb i l n y a 2 b o l a me r a h d a n 1
b o l a h i j a u . Pa d a s o a l

Se h i n g g a , p e l u a n g d a r i
k e j a d i a n C d a p a t d i t e n t u k a n
s e p e r t i b e r i k u t .
J a d i , p e l u a n g t e r a mb i l n y a 2
b o l a b e r w a r n a me r a h d a n 1 b o a l
b e r w a r n a h i j a u a d a l a h 1/6.

4. D 1 : A = k e j a d i a n s e o r a n g a n a k
t e r k e n a s u a t u p e n y a k i t
N = 1000
D 2 : f h (A) ….. ?
D3 :
P (s e o r a n g a n a k t e r k e n a s u a t u
p e n y a k i t ) = 0,15
P( s e o r a n g a n a k t i d a k t e r k e n a
s u a t u p e n y a k i t ) = 1 – P (s e o r a n g
a n a k t e r k e n a p e n y a k i t )
= 1 – 0,15
= 0,85
F h (A ) = p (A ) x N
= 0,85 x 1000
= 850
J a d i , a n a k y a n g d i p e r k i r a k a n
t i d a k t e r k e n a p e n y a k i t a d a l a h
850 o r a n g

5. P (d u a g a m b a r s a t u a n g k a ) = 1/4,
ma k a
F h = P (A ) x b a n y a k p e r c o b a a n
= 1/4 x 40
= 10 (A )

Peluang suatu kejadian kelompok 7

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Peluang suatu kejadian kelompok 7