Question

Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). (Enter your answers as a comma-separated list. Enter ∅ for the empty set.)
(a) What are the 16 outcomes in ?
(b) Which outcomes are in the event that exactly three of the selected mortgages are fixed rate?
(c) Which outcomes are in the event that all four mortgages are of the same type?
(d) Which outcomes are in the event that at most one of the four is a variable-rate mortgage?
(e) What is the union of the events in parts (c) and (d)?
What is the intersection of these two events?
(f) What is the union of the two events in parts (b) and (c)?
What is the intersection of the two events in parts (b) and (c)?

Answer 1

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.

Answer 2

Sample of four homes.

The sample of 4 homes is on a mortgage and has been classified as a fixed rate of F and a variable rate of V. The mortgage is thus an agreement between the lender of the money and the borrower. The lender has the right to take away the property.

Thus answer is given below.

• The set of 16 outcomes of the variable and the fixed rates is given as {FVVV,FFVV,VFVV,VVVV,FVFV,FFFV,VFFV, and VVFV,FVVF,FFVF,VFVF,VVVF,and

• the FVFF,FFFF,VFFF,VVFF}. The outcomes in the events that exactly is of 3 of the selected mortgages at a fixed rate is about {FFFV, FFVF,FVFF, VFFF}

• The outcomes of the events that all four mortgages are of the same type are about {FFFF, VVVV} The union of events in parts of c and d are as {FFFV, FFVF, FVFF, FFFF, VFFF}.

Learn more about the sample of four homes.

brainly.com/question/14565659.