-.~
Name
(Review of 3.3)
r-".
Independent
v
p(AIB)
Events:
= P(A);
p(BIA)
= P(B);
Addition Property:
P(A U B) = P(A) + P(B) - P(A
Mutually Exclusive: P(A B) = 0;
n
CD
IfP(A)
= y"
P(B)
=
= p.
1/3 and P(A U B)
8)
n B)
Find P if:
b) A and B are independent.
2) If P(A)
.34
= 3.,
~
'11-\1I5 -,V/2' IhJ
= ~ and
P(B)
B) ;
\h.. t\j:, -:::~
-=--
~lf-\J\?)':
= P(Ap~~~B) ; p(BIA) = P(Ap~~
I~
a) A and B are mutually exclusive
rCAv
p(AIB)
P(A U B)
= p.
.
=-l~
Find p if:
a) A and B are mutually exclusive
b) A and B are independent.
1.-hrll~
rlAJ()):
GIf
P(R);; 0.4, P(S) = 0.5 and P(R U S)
v'l ~,v")~
I~
t.)
-
.
4) If P(A)
t. 1..:: . ~
. a) P(A
2
= -,
n B)
3
P(B)
'lAAe} " f(~)\ ?l\3) .
1-1'b
'-..
:
Rand S independent events?
l\~
to • S') '- .7
Y Q.. <.,
'. 3) If P(H) = 0.6, P(M) = 0.2, and P(H
(10
= 0.7 ,are
I
= -,
3..
P(A
U M) = 0.8,
!"\l!.fH-s
1
U B) = -,
~
find:
2
b) p(AIB)
m]0 ~lA\\?')
='
r \13 - '12. - '/2.
Are A and B independent events'!
are H and M dependent events?
CJo.fC!.
r.':
'6
sc\
e¥
5
'JGe \ n ( p
I
d('p~
. I
3
) If P(A)=-,P(B)=-,P(AUB)=-,
a) P(A
n B)
3
4
5
..
6
find:
c) p(BIA)
b) P(AjB)
\ \l\.J
- '}
\1t.t.IIj~-:::
3h- .3
1(4
..Are A and B independent events?
6) IfP(X)
= 0.5, P(Y) = 0.7, and
X and Y are independent events, detennine the probability of the occurrence
of:
,S .,1 ~I:!>S\
,S .,.~l-(.1' .~)~
d) X but not Y
?L)( n ~l)
,~;'.vl"]j
c) neither X nor Y
b) X or Y
a) both X and Y
.~)
e) X given that Y occurs.
.
H/) :::IlL>'- I f)
r:;\
7) If P(K) =.003, P(R);= 0.8, and K and R are ~ent
of:
.
?l" 1\ 12..) =. 3 '. ~-::,1-4
~ L {2
f)
KtJ
.t '.l ::[}bJ
.
.
events, detennine the probability of the occurrence
a) both K and R
d) R but not K
\-.~')::Q3
e) R given that K occurs.
r L rz-,( k) ::.-e ()2,J
l~