MATH 3081 Homework 2 Due date: January 19, 2024
2.3.1 According to a family-oriented lobbying group, there is too much crude language and violence on television.
Forty-two percent of the programs they screened had language they found o↵ensive, 27% were too violent, and
10% were considered excessive in both language and violence. What percentage of programs did comply with the
groups standards?
42 10
A: offensive AlB :·
S
.
Y
.
B: Violent .
27
17
31
·
.
Assume n(s) 100
p(s) 1 :
:
100 -
1 320
.
·
If .
17)
1
did
comply %
2.3.2 Let A and B be any two events defined on S. Suppose that P (A) = 0.4, P (B) = 0.5, and P (A \ B) = 0.1. What
is the probability that A or B but not both occur?
S P (( n B4u(A) nB)) = p(AnB) p(AinB) =
A B
· 2
= 3 +.
4 = /
3 1
. .
4
⑮
2.3.4 Let A and B be any two events defined on S. If the probability that at least one of them occurs is 0.3 and the
probability that A occurs but B does not occur is 0.1, what is P (B)?
↓ P(Au Bl : 3
S
pCARB)
A
didn't say =
mir
-
·
I only" B
1- p(ArB) : 7
O
T
P(B) 20 %
.
= 2
·
:
2.3.1 According to a family-oriented lobbying group, there is too much crude language and violence on television.
Forty-two percent of the programs they screened had language they found o↵ensive, 27% were too violent, and
10% were considered excessive in both language and violence. What percentage of programs did comply with the
groups standards?
42 10
A: offensive AlB :·
S
.
Y
.
B: Violent .
27
17
31
·
.
Assume n(s) 100
p(s) 1 :
:
100 -
1 320
.
·
If .
17)
1
did
comply %
2.3.2 Let A and B be any two events defined on S. Suppose that P (A) = 0.4, P (B) = 0.5, and P (A \ B) = 0.1. What
is the probability that A or B but not both occur?
S P (( n B4u(A) nB)) = p(AnB) p(AinB) =
A B
· 2
= 3 +.
4 = /
3 1
. .
4
⑮
2.3.4 Let A and B be any two events defined on S. If the probability that at least one of them occurs is 0.3 and the
probability that A occurs but B does not occur is 0.1, what is P (B)?
↓ P(Au Bl : 3
S
pCARB)
A
didn't say =
mir
-
·
I only" B
1- p(ArB) : 7
O
T
P(B) 20 %
.
= 2
·
:
