Answer:
a)
{FVVV,FFVV,VFVV,VVVV,FVFV,FFFV,VFFV,VVFV,FVVF,FFVF,VFVF,VVVF,FVFF,FFFF,VFFF,VVFF}
b)
{FFFV,FFVF,FVFF,VFFF}
c)
{FFFF,VVVV}
d)
{FFFV,FFVF,FVFF,FFFF,VFFF}
e)
{FFFV,FFVF,FVFF,FFFF,VFFF,VVVV}
{FFFF}
f)
{FFFV,FFVF,FVFF,VFFF,FFFF,VVVV}
{ }
Step-by-step explanation:
a)
The 16 outcomes for a sample of four home mortgages classified as fixed and variable rate are
Sr.No Outcomes
1 FVVV
2 FFVV
3 VFVV
4 VVVV
5 FVFV
6 FFFV
7 VFFV
8 VVFV
9 FVVF
10 FFVF
11 VFVF
12 VVVF
13 FVFF
14 FFFF
15 VFFF
16 VVFF
b)
Let A be the event that exactly three are fixed rate. Thus, event A consists of following outcomes
A={FFFV,FFVF,FVFF,VFFF}
c)
Let B be the event that all four are of same type. The event B consists of either all fixed rate or all variable rate. Thus, event B consists of following outcomes
B={FFFF,VVVV}
d)
Let C be the event that at most one of four is variable rate. The event C consists of less than and equal to one variable rate. Thus, event C consists of following outcomes
C={FFFV,FFVF,FVFF,FFFF,VFFF}
e)
Let union of part(c) and part(d) can be represented as BUC. The union represents all the outcomes in event B and event C.
B∪C={FFFF,VVVV}∪{FFFV,FFVF,FVFF,FFFF,VFFF}
B∪C={FFFV,FFVF,FVFF,FFFF,VFFF,VVVV}
Let intersection of part(c) and part(d) can be represented as B∩C. The intersection represents the common outcomes in event B and event C.
B∩C={FFFF,VVVV}∩{FFFV,FFVF,FVFF,FFFF,VFFF}
B∩C={FFFF}
f)
Let union of part(b) and part(c) can be represented as AUB. The union represents all the outcomes in event A and event B.
A∪B={FFFV,FFVF,FVFF,VFFF}∪{FFFF,VVVV}
A∪B={FFFV,FFVF,FVFF,VFFF,FFFF,VVVV}
Let intersection of part(b) and part(c) can be represented as A∩B. The intersection represents the common outcomes in event A and event B.
A∩B={FFFV,FFVF,FVFF,VFFF}∩{FFFF,VVVV}
A∩B={ }
So intersection of part(b) and part(c) is an empty set as there is no common outcome in these two sets.
