Exercises Course Titel probability and S
Exercises
Prepared By :
Rayan Aram Baram
ID: 311156005
Date : 16-5-2017
Thuesday
College of Science and Technology
Department of Computer Science
Morning Second Semenster
Course Titel : probability and Statistics
Exercises chapter 1
1-
( ). ( )
( )=
( )=
( )=
( )( )
=
=
( )( )
= 35
= 21
( )
( )
=
( )=
(35*15)+(35*6)+(21*1) = 756 (D)
2LEADING
5!= 5*4*3*2*1=120 (D)
3!= 3*2*1 = 6
120*6= 720 (C)
3CORPORATION
= 50400
(D)
4( )
=
( )
35*6=210 (A)
5LEADER = 6!
=
6-
= 360 (C)
= 35
7DETAIL 3*3*2*2*1*1=36 (B)
8( )=
=
( )=
= 84
= 20
84-20=64 (A)
9(2,3,5,6,7) = 5!
=20 (A)
10- 1*1*8*7*6*5=1680 (D)
Exercises chapter 2
1A- P(A|B) =
B- P(B|A) =
C- P(A ∪ B) = P(A)+P(B)-P(AB)
=
c
+
-
=
c
D-P(A |B ) =
c
c
E- P(B |A ) = =
2AB-
=
=
=
=
3A- Dice = { (5,1),(1,5),(4,2),(2,4) } =
B- Dice = { (1,2),(1,3),(1,4),(1,5),(1,6) }
=
C- Dice = { (1,2),(2,1),(1,3),(3,1) }
==
4-
=
= 0.03
5A- =
-
=
B- =
-
=
C-= P(A ∪ B) =
6-
( )
( ) ( )
( )
+
=
-
=1
= 0.021
=
7A-
=
B-
8Pr(x = R) = ( )
( )( ) (
3*
*
)
9A- {HH, TH, HT, TT}. Only 2 of those, TH and HT,
B- Same 4 possibilities -- but only HH works.
C- 2 possibilities are T, H. Only T works,
=
.
.
D- doesn't matter which order the coins are thrown
10A- Dice = { (4,4),(4,5),(4,6) }
=
=
B-Dice = {(4,4),(4,5),(4,6),(5,5),(5,4),(5,6),(6,6),(6,5),(6,4) }
=
C- We don t have probability
D- Dice = { (2,6),(3,5),(3,6),(4,4),(4,5),(4,6) }
=
=
11- {
P(
T}1.3|{H}1)
{
=
}
=
=
= P({HT}2,3)
= ( ) P(H)P(T) =
=8
(H H H) (H H T) (H T H) (H T T) (T H H) (T H T)
(T T H) (T T T)
{0 heads} = {TTT}
{1 head} = {HTT,THT,TTH}
P({1head} =
12P(X = k) =
( )(
P(X = 2) =
( )( )
P(X = 2) =
( )
( )
)
=
P(X = 2) = (4C1* )* (3C1* )
P(X = 2) =
*
=
Prepared By :
Rayan Aram Baram
ID: 311156005
Date : 16-5-2017
Thuesday
College of Science and Technology
Department of Computer Science
Morning Second Semenster
Course Titel : probability and Statistics
Exercises chapter 1
1-
( ). ( )
( )=
( )=
( )=
( )( )
=
=
( )( )
= 35
= 21
( )
( )
=
( )=
(35*15)+(35*6)+(21*1) = 756 (D)
2LEADING
5!= 5*4*3*2*1=120 (D)
3!= 3*2*1 = 6
120*6= 720 (C)
3CORPORATION
= 50400
(D)
4( )
=
( )
35*6=210 (A)
5LEADER = 6!
=
6-
= 360 (C)
= 35
7DETAIL 3*3*2*2*1*1=36 (B)
8( )=
=
( )=
= 84
= 20
84-20=64 (A)
9(2,3,5,6,7) = 5!
=20 (A)
10- 1*1*8*7*6*5=1680 (D)
Exercises chapter 2
1A- P(A|B) =
B- P(B|A) =
C- P(A ∪ B) = P(A)+P(B)-P(AB)
=
c
+
-
=
c
D-P(A |B ) =
c
c
E- P(B |A ) = =
2AB-
=
=
=
=
3A- Dice = { (5,1),(1,5),(4,2),(2,4) } =
B- Dice = { (1,2),(1,3),(1,4),(1,5),(1,6) }
=
C- Dice = { (1,2),(2,1),(1,3),(3,1) }
==
4-
=
= 0.03
5A- =
-
=
B- =
-
=
C-= P(A ∪ B) =
6-
( )
( ) ( )
( )
+
=
-
=1
= 0.021
=
7A-
=
B-
8Pr(x = R) = ( )
( )( ) (
3*
*
)
9A- {HH, TH, HT, TT}. Only 2 of those, TH and HT,
B- Same 4 possibilities -- but only HH works.
C- 2 possibilities are T, H. Only T works,
=
.
.
D- doesn't matter which order the coins are thrown
10A- Dice = { (4,4),(4,5),(4,6) }
=
=
B-Dice = {(4,4),(4,5),(4,6),(5,5),(5,4),(5,6),(6,6),(6,5),(6,4) }
=
C- We don t have probability
D- Dice = { (2,6),(3,5),(3,6),(4,4),(4,5),(4,6) }
=
=
11- {
P(
T}1.3|{H}1)
{
=
}
=
=
= P({HT}2,3)
= ( ) P(H)P(T) =
=8
(H H H) (H H T) (H T H) (H T T) (T H H) (T H T)
(T T H) (T T T)
{0 heads} = {TTT}
{1 head} = {HTT,THT,TTH}
P({1head} =
12P(X = k) =
( )(
P(X = 2) =
( )( )
P(X = 2) =
( )
( )
)
=
P(X = 2) = (4C1* )* (3C1* )
P(X = 2) =
*
=