Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). (Enter your answers in set notatio

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

A sample of 4 mortgages has been chosen.

Part a

We have 2*2*2*2= 16 possible combinations shown below:

FFFF, FVFF, FFVF, FFFV,

FVFV, FFVV,FVVF,VVFF,

VFVF, VVFF,VFFV,FFVV

VVVV, VFVV, VVFV, VVVF

Part b

Identify the outcomes when exactly three of the selected mortgages are fixed-rate

We must verify from the outcomes listed in part a how many feature exactly three F's. The suitable combinations are:

FVFF, FFVF, FFFV, VFFF

Part c

What are the outcomes when all four mortgages are identical?[TAG_65]]

Here, we have merely two matching values: VVVV or FFFF

Part d

Identify outcomes when at most one of the four is variable-rate mortgage.

We need to verify in the possible outcomes from part a) how many include at least one V. After analysis, the valid combinations are:

FFFF, FVFF, FFVF, FFFV, VFFF

Part e

The union represents all four mortgages are of the same classification or the outcomes where at most one among the four is a variable-rate. Thus, we are seeking outcomes VVVV and FFFF, along with combinations featuring one V (FVFF, FFVF, FFFV, VFFF) leading to the union:

FFFF, FVFF, FFVF, FFFV,VFFF, VVVV