Peluang suatu kejadian kelompok 7

31

Transcript of Peluang suatu kejadian kelompok 7

Page 1: Peluang suatu kejadian kelompok 7
Page 2: Peluang suatu kejadian kelompok 7
Page 3: Peluang suatu kejadian kelompok 7

P e l u a n g s u a t u

k e j a d i a n• P e 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 ut i n d a k a n a t a u k e g i a t a ny a n g d a p a t m e m b e r i k a nb e b e r a p a k e m u n g k i n a n h a s i l• R u a n g S a m p e l :

r u a n g s a m p e l a d a l a h

h i m p u n a n s e m u a h a s i l y a n g

m u n g k i n d a r i s u a t u

p e r c o b a a n• K e j a d i a n :

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 m p 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

Page 4: Peluang suatu kejadian kelompok 7

Contoh:s e p u l u h k a r t u i d e n t i kd i b e r i n o m o r 0, 1, 2, 3,…, 9 d a n d i t e m p a t k a n d a l a ms e b u a h k o t a k t e r t u t u pd i a m b i l s a t u k a r t us e c a r a a c a k d a nm e n g a m a t i n o m o r k a r t u

y a n g t e r a m b i l .R u a n g s a m p e l S = ,9,8,7,6,5,4,3,2,1,0

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 ay a n g m u 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 m p e l a t a u

a n g g o t a r u a n g s a m p e lS e m b a r a n g h i m p u n a n b a g i a n d a l a m

r u a n g s a m p e l d i n a m a k a n k e j a d i a n a t a u

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 m b i l b e r n o m o r g a n j i l

9,7,5,3,1

Page 5: Peluang suatu kejadian kelompok 7

T e o r e m a

J i k a r u a n g s a m p e l St e r d i r i d a r i t i t i k -t i t i k s a m p e l y a n gs e r u p a s e h i n g g a m a s i n g -m a s i n g m e m p u n y a ip e l u a n g y a n g s a m a d a n Ea d a l a h k e j a d i a n y a n gd i h a r a p k a n t e r j a d im a k a :

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

)(

)()(

Sn

EnEP

Page 6: Peluang suatu kejadian kelompok 7

Contoh:

• P e r c o b a a n

p e n g a m b 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 m o r 0, 1, 2, 3, …, 9.

11

E a d a l a h k e j a d i a n

t e r a m b i l k a r t u

b e r n o m o r 1B e r a p a p e l u a n g t e r a m b i l k a r t u

b e r n o m o r 1?S e t i a p k a r t u i d e n t i k , s e h i n g g a

s e t i a p k a r t u m e n d a p a t p e l u a n g y a n g

s a m a u n t u k t e r p i l i h .

B a n y a k a n g g o t a E 1 a t a u n (E 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 (S ) = 10

10

1

)(

)()(

1

1Sn

EnEP

P e l u a n g t e r a m b i l

k a r t u b e r n o m o r 1

a d a l a h :

Page 7: Peluang suatu kejadian kelompok 7

Contoh:

• P e r c o b a a n p e n g a m b 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 m o r

0, 1, 2, 3, …, 9.9,7,5,3,1

2E a d a l a h k e j a d i a n

t e r a m b i l k a r t u

b e r n o m o r g a n j i lB e r a p a p e l u a n g t e r a m b i l k a r t u

b e r n o m o r g a n j i l ?S e t i a p k a r t u i d e n t i k , s e h i n g g a

s e t i a p k a r t u m e n d a p a t p e l u a n g

y a n g s a m a u n t u k t e r p i l i h .

B a n y a k a n g g o t a E 2 a t a u n (E 2)= 5

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 (S ) = 10P e l u a n g t e r a m b i l

k a r t u b e r n o m o r g a n j i l

a d a l a h :

2

1

10

5

)(

)()(

2

2Sn

EnEP

Page 8: Peluang suatu kejadian kelompok 7

Contoh:• P e r c o b a a n p e n g a m b 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 m o r

0, 1, 2, 3, …, 9. 9,8,7,6,5,4,3,2,1,03

E

a d a l a h k e j a d i a n t e r a m b i l k a r t u

b e r n o m o r 0,1,2,3,…, a t a u 9

Berapa peluang terambil kartu bernomor 0, 1,2,3, …,9?

S e t i a p k a r t u i d e n t i k , s e h i n g g a s e t i a p

k a r t u m e n d a p a t p e l u a n g y a n g s a m a

u n t u k t e r p i l i h .

B a n y a k a n g g o t a E 3 a t a u n (E 3)= 10

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 (S ) = 10

P e l u a n g t e r a m b i l

k a r t u b e r n o m o r g a n j i l

a d a l a h :

110

10

)(

)()(

3

3Sn

EnEP

Page 9: Peluang suatu kejadian kelompok 7

Contoh:

• P e r c o b a a n p e n g a m b 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 m o r

0, 1, 2, 3, …, 9.4E

a d a l a h k e j a d i a n t e r a m b i l k a r t u

b e r n o m o r 10Berapa peluang terambil kartu bernomor 10?

S e t i a p k a r t u i d e n t i k , s e h i n g g a s e t i a p

k a r t u m e n d a p a t p e l u a n g y a n g s a m a

u n t u k t e r p i l i h .

B a n y a k a n g g o t a E 4 a t a u n (E 4)= 0

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 (S ) = 10

P e l u a n g t e r a m b i l

k a r t u b e r n o m o r 10

a d a l a h :

010

0

)(

)()(

4

4Sn

EnEP

Page 10: Peluang suatu kejadian kelompok 7

K i 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 nM i s a l k a n S a d a l a h

r u a n g s a m p e l d a n E

a d a l a h k e j a d i a n

y a n g d i h a r a p k a n

t e r j a d i

SEmakaEdariSEKarena ,

)()()( SnEnnsehingga

)(

)(

)(

)(

)(

)(

Sn

Sn

Sn

En

Sn

n

1)(0 EP

P (E ) = 0, m a k a k e j a d i a n E d i s e b u t

k e j a d i a n y a n g t i d a k m u n g k i n

t e r j a d iP (E ) = 1, m a k a k e j a d i a n E d i s e b u t

k e j a d i a n y a n g p a s t i t e r j a d i

Page 11: Peluang suatu kejadian kelompok 7

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 .

T e n t u k a n :

a . r u a n g s a m p e l

p e r c o b a a n t e r s e b u t

d a n

j u m l a h a n g g o t a

r u a n g s a m p e l .

b . p e l u a n g m u n c u l

m a t a d a d u g a n j i l

Page 12: Peluang suatu kejadian kelompok 7

P e m b a h a s a n :

a .R u a n g s a m p e l

3,2,12

E

,6,5,4,3,2,1S

b . m i 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

6)(Sn

5,3,11

E 3)(1

En2

1

6

3

)(

)()(

1

1Sn

EnEP

J a d i p e l u a n g m u n c u l

m a t a d a d u g a n j i l

a d a l a h

J u m l a h a n g g o t a

r u a n g s a m p e l

c . M i s a l E 2 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 k u r a n g d a r i

4 3)(2

En2

1

6

3

)(

)()(

2

2Sn

EnEP

2

1

J a d i p e l u a n g m u n c u l m a t a

d a d u k u r a n g d a r i 4 a d a l a h :2

1

Page 13: Peluang suatu kejadian kelompok 7

Contoh:

1. D u a u a n g l o g a m

d i l e m p a r b e r s a m a -

s a m a s a t u k a l i .

T e n t u k a n p e l u a n g :

a . m u n c u l n y a s a t u

s i s i g a m b a r

b . m u n c u l n y a d u a

g a m b a r

Page 14: Peluang suatu kejadian kelompok 7

Pembahasan:

• R u a n g s a m p e l),(),,((),,(),,( GGAGGAAAS

4)(Sn

a . M i 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 n y a s a t u s i s i g a m b a r),((),,(

1AGGAE 2)(

1En

2

1

4

2

)(

)()(

1

1Sn

EnEP J a d i p e l u a n g

m u n c u l

s a t u s i s i

g a m b a r

a d a l a h

2

1

b . M i s a l E 2 a d a l a h k e j a d i a n

m u n c u l d u a g a m b a r),(

2GGE 1)(

2En

4

1

)(

)()(

2

2Sn

EnEP

J a d i p e l u a n g m u n c u l

d u a s i s i g a m b a r a d a l a h 4

1

Page 15: Peluang suatu kejadian kelompok 7

S o a l :

D a r i d a l a m s e b u a h k o t a kt e r d a p a t 4 k e l e r e n gm e 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 ud i a m b i l s e c a r a a c a k 3k e l e r e n g s e k a l i g u s .T e n t u k a n p e l u a n gk e l e r e n g y a n g t e r a m b i lt e r d i r i d a r i :

a . 2 k e l e r e n g m e r a h d a n 1

k e l e r e n g b i r ub . 1 k e l e r e n g 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 . K e t i g a n y a b e r w a r n a

m e r a h

Page 16: Peluang suatu kejadian kelompok 7

J a w a b :

a . B a n y a k k e l e r e n g

s e l u r u h n y a a d a 9

• B a n y a k c a r a p e n g a m b i l a n 3

k e l e r e n g s e k a l i g u s d a r i

d a l a m k o t a k a d a l a h

.

84!3!6

!939

C

J a d i j u m l a h s e m e s t a p a d a

p e n g a m b i l a n t i g a d a r i

s e m b i l a n k e l e r e n g a d a l a h84)(Sn

• a d a 4 k e l e r e n g m e r a h

s e h i n g g a b a n y a k c a r a

p e n g a m b i l a n 2 k e l e r e n g m e r a h

d a r i d a l a m k o t a k a d a6!2!2

!424

C

s e d a n g k a n b a n y a k c a r a

p e n g a m b i l a n 1 k e l e r e n g b i r u

a d a l a h 3!1!2

!313

C

Page 17: Peluang suatu kejadian kelompok 7

J a w a b (l a n j u t a n )

• B a n y a k c a r a p e n g a m b i l a n 2

k e l e r e n g m e r a h d a n 1

k e l e r e n g b i r u a d a l a h

s e h i n g g a

P (2m ,1b ) =

183.61324

CC

14

3

84

18

b. D e n g a n c a r a y a n g s a m a p e l u a n g

t e r a m b i l 1 k e l e r e n g 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 a d a l a h : P (1m ,1b , 1h ) =

7

2

84

2.3.4

39

121314

C

CCC

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 e n g t e r s e b u t m e r a h

a d a l a h :P (3m ) = 21

1

84

4

39

34

C

C

Page 18: Peluang suatu kejadian kelompok 7

F r e k u e n s i

h a r a p a n• F r e k u e n s i h a r a p a n

s u a t u k e j a d i a n p a d ap e r c o b a a n y a n gd i l a k u k a n N k a l i a d a l a hh a s i l k a l i p e l u a n gk e j a d i a n t e r s e b u td e n g a n b a n y a k n y ap e r c o b a a n .

d i r u m u s k a n s e b a g a i :

)()( EPNEFh

C o n t o h :

D u a d a d u d i l e m p a r b e r s a m a a n

s e b a n y a k 36 k a l i . T e n t u k a n

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

m u n c u l n y a m a t a d a d u

b e r j u m l a h 11 a t a u 12

Page 19: Peluang suatu kejadian kelompok 7

• J a w a b :

M i s a l k a n E a d a l a h

k e j a d i a n m u n c u l j u m l a h

m a t a d a d u 11 a t a u 12, m a k a

C o n t o h :D u a d a d u d i l e m p a r b e r s a m a a n

s e b a n y a k 36 k a l i . T e n t u k a n

f r e k u e n s i h a r a p a n m u n c u l n y a

m a t a d a d u b e r j u m l a h 11 a t a u 12

3)( ;)6,6(),6,6(),6,5( EnE

kaliEPNFSn

EnEP

h 3

12

136)( ,

12

1

36

3

)(

)()(

Page 20: Peluang suatu kejadian kelompok 7

K e j a d i a n

M a j e m u kK o m p l e m e n s u a t u

k e j a d i a n E d i t u l i s

E c a d a l a h k e j a d i a n

t i d a k t e r j a d i n y a EC o n t o h :

M i s a l k a n p a d a p e r c o b a a n

m e n g a m b i l s a t u k a r t u d a r i

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

n o m o r 1,2,3,4,5,6,7,d a n 8 d a r i

d a l a m s e b u a h k o t a k8,7,6,5,4,3,2,1S

4 bernomor kartu erambilkejadian tadalah 3,2,1 Ejika

c

E : K e j a d i a n t i d a k

t e r a m b i l k a r t u <

4 8,7,6,5,4c

E

Page 21: Peluang suatu kejadian kelompok 7

H u b u n g a n a n t a r a )(dan )(c

EPEP

1)(

)(

)(

)(

)(

)()()(

Sn

Sn

Sn

ESn

Sn

EnEPEP

c

)(1)( EPEPc

P a d a p e r c o b a a n d i a t a s

8

5)(dan

8

3)(

cEPEP

Page 22: Peluang suatu kejadian kelompok 7

S o a l :

S e b u a h k o t a k b e r i s i 5

b o l a m e r a h , 3 b o l a

p u t i h , d a n 2 b o l a

k u n i n g . T e n t u k a n

p e l u a n g t e r a m b i l b o l a

b u k a n k u n i n g

J a w a b :

S e l u r u h n y a a d a 10 k e l e r e n g

n (s )=10

M i s a l K a d a l a h k e j a d i a n

t e r a m b i l k e l e r e n g k u n i n g ,

k e l e r e n g k u n i n g a d a 2, m a k a

n (K )= 25

1

10

2

)(

)()(

Sn

KnKP

kuningbukan kelereng erambilkejadian t :c

K

5

4)(1)( KPKP

C

Page 23: Peluang suatu kejadian kelompok 7

K e j a d i a n

m a j e m u k

• M i s a l k a n E 1 d a n E 2

a d a l a h d u a k e j a d i a n

p a d a p e r c o b a a n y a n g

s a m a :

)(

)()()(

)(

)()(

212121

21Sn

EEnEnEn

Sn

EEnEEP

)()()()(212121

EEPEPEPEEP …(1)

Page 24: Peluang suatu kejadian kelompok 7

D u a k e j a d i a n

s a l i n g l e p a s

• D u a k e j a d i a n y a n g

s a l i n g l e p a s (s a l i n g

a s i n g :d i s j o i n t )

m e r u p a k a n d u a

k e j a d i a n y a n g t i d a k

d a p a t t e r j a d i

s e c a r a b e r s a m a a n

21EE

0)(

)()(

21

21Sn

EEnEEP

S e h i n g g a (1) m e n j a d i : )()()(2121

EPEPEEP

Page 25: Peluang suatu kejadian kelompok 7

D u a k e j a d i a n

s a l i n g b e b a s

• D u a k e j a d i a n y a n g

s a l i n g b e b a s

a r t i n y a k e j a d i a n

y a n g s a t u t i d a k

m e m p e n g a r u h i

k e j a d i a n y a n g l a i n

• D u a k e j a d i a n E 1 d a n E 2

s a l i n g b e b a s j i k a

d a n h a n y a j i k a

)()()(2121

EPEPEEP

Page 26: Peluang suatu kejadian kelompok 7

L a t i h a n

1. S e b u a h d a d u d i l e m p a r

s a t u k a l i . B e r a p a b e s a r

p e l u a n g m u n c u l n y a m a t a

d a d u b i l a n g a n p r i m a ?

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 m b i l s e b u a h

k a r t u s e c a r a a c a k .

B e 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 A s ?

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

t e r d i r i d a r i 5 b o l a w a r n a

Page 27: Peluang suatu kejadian kelompok 7

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 m a d i l e m p a r b e r s a m a -

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 m u n c u l n y a 2 g a m b a r

d i s e b e l a h a t a s a d a l a h ...

Page 28: Peluang suatu kejadian kelompok 7

P e m b a h a s a n1. 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

m a t a d a d u b i l a n g a n p r i m a

d i s i m b o l k a n d e n g a n A , m a 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 m u n c u l n y a m a 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 m b 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 m u 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 m b i l n y a 2 b o l a m e r a h d a n 1

b o l a h i j a u . P a d a s o a l

d i k e t a h u i b a h w a b a n y a k b o l a

Page 29: Peluang suatu kejadian kelompok 7

S e 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 m b i l n y a 2

b o l a b e r w a r n a m e 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.

Page 30: Peluang suatu kejadian kelompok 7

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) ….. ?

D 3 :

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

Page 31: Peluang suatu kejadian kelompok 7

5. P (d u a g a m b a r s a t u a n g k a ) = 1/4,

m a 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 )