MATH 3081 Homework 3 Due date: January 26, 2024
Name: Max
Langweil
2.4.1 Suppose that two fair dice are tossed. What is the probability that the sum equals 10 given that it exceeds 8?
A : Sum a
exceeds p(BIA) :
PB) I
=
B P(A)
: Sum equals lo
123456
1 ,4 1, 5 1,6
i 1 l ,
1 .2 1,3
1 2 , 22 , 3 2 , 42 , 5 2, 6
2 .
3 6
3 23, it is.
! .
4 ,6
4,
5,
E Gil 6,2 6 36416
,
, 5 Gib
2.4.2 Find P (A \ B) if P (A) = 0.2, P (B) = 0.4, and P (A|B) + P (B|A) = 0.75.
P(AIB) :
PANB) p(AIB) = . 7 5 -
p(B)A)
PCB) PCB
PACB
75
-
.
=
AnB) PB)
P(B)
_
PCA)
= .
75
P(AnB)
it is A
P(AnB) ( ,) :
(a) : .
75
O
=.
2.4.7 (Not graded) An urn contains one red chip and one white chip. One chip is drawn at random. If the chip selected
is red, that chip together with two additional red chips are put back into the urn. If a white chip is drawn, the
chip is returned to the urn. Then a second chip is drawn. What is the probability that both selections are red?
z
↑
chips
ships ↑ P(R , 1 Ra) =
p(Ra(R) p(R) :
.
=
R W
/N
M
-
W
R
RR
2.4.12 A fair coin is tossed three times.What is the probability that at least two heads will occur given that at most two
heads have occurred? :
A : at least I heads ST ITH IHH ,
, ,
HHH3
B : at most I headS Occur : SHHT HTH ,THH HTT
TTH THT TT
,
, , , ,
P(A/B) B) 3/s
8
:
=
: I
P(B)
Name: Max
Langweil
2.4.1 Suppose that two fair dice are tossed. What is the probability that the sum equals 10 given that it exceeds 8?
A : Sum a
exceeds p(BIA) :
PB) I
=
B P(A)
: Sum equals lo
123456
1 ,4 1, 5 1,6
i 1 l ,
1 .2 1,3
1 2 , 22 , 3 2 , 42 , 5 2, 6
2 .
3 6
3 23, it is.
! .
4 ,6
4,
5,
E Gil 6,2 6 36416
,
, 5 Gib
2.4.2 Find P (A \ B) if P (A) = 0.2, P (B) = 0.4, and P (A|B) + P (B|A) = 0.75.
P(AIB) :
PANB) p(AIB) = . 7 5 -
p(B)A)
PCB) PCB
PACB
75
-
.
=
AnB) PB)
P(B)
_
PCA)
= .
75
P(AnB)
it is A
P(AnB) ( ,) :
(a) : .
75
O
=.
2.4.7 (Not graded) An urn contains one red chip and one white chip. One chip is drawn at random. If the chip selected
is red, that chip together with two additional red chips are put back into the urn. If a white chip is drawn, the
chip is returned to the urn. Then a second chip is drawn. What is the probability that both selections are red?
z
↑
chips
ships ↑ P(R , 1 Ra) =
p(Ra(R) p(R) :
.
=
R W
/N
M
-
W
R
RR
2.4.12 A fair coin is tossed three times.What is the probability that at least two heads will occur given that at most two
heads have occurred? :
A : at least I heads ST ITH IHH ,
, ,
HHH3
B : at most I headS Occur : SHHT HTH ,THH HTT
TTH THT TT
,
, , , ,
P(A/B) B) 3/s
8
:
=
: I
P(B)
