Answer:
a) FFFF, FVFF, FFVF, FFFV,
FVFV, FFVV,FVVF,VVFF,
VFVF, VFFF,VFFV,FFVV
VVVV, VFVV, VVFV, VVVF
b) FVFF, FFVF, FFFV,VFFF
c) VVVV or FFFF
d) FFFF, FVFF, FFVF, FFFV, VFFF
e) FFFF, FVFF, FFVF, FFFV ,VFFF, VVVV
Step-by-step explanation:
For this case we define some notation:
F= mortgage classified as fixed rate
V= mortgage classified as variable rate
We select a sample of 4 mortgages.
Part a
We have 2*2*2*2= 16 possible combinations defined below:
FFFF, FVFF, FFVF, FFFV,
FVFV, FFVV,FVVF,VVFF,
VFVF, VVFF,VFFV,FFVV
VVVV, VFVV, VVFV, VVVF
Part b
Which outcomes are in the event that exactly three of the selected mortgages are fixed rate
We need to see in the possible outcomes from part a) how many we have exactly three F's .If we analyze the possible options the possible combinations are:
FVFF, FFVF, FFFV, VFFF
Part c
Which outcomes are in the event that all four mortgages are of the same type?
For this case we have just two possible values: VVVV or FFFF
Part d
Which outcomes are in the event that at most one of the four is a variable rate mortgage?
We need to see in the possible outcomes from part a) how many have at least one V. After analyze we see that the possible values:
FFFF, FVFF, FFVF, FFFV, VFFF
Part e
The union represent all four mortgages are of the same type or outcomes are in the event that at most one of the four is a variable rate. So we are looking for the possible outcomes VVVV and FFFF and the outcomes with just one V ( FVFF, FFVF, FFFV ,VFFF) so then the union would be:
FFFF, FVFF, FFVF, FFFV ,VFFF, VVVV
