Question

Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V).

a) What are the 16 outcomes in sample space?

b) Which outcomes are in the event that exactly three of the selected mortgages are fixed rates?

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), and what is the intersection of these two events?

f) What are the union and intersection of the two events in parts (b) and (c)?

Answer 1

Answer:-

Given that:-

Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V).

a) What are the 16 outcomes in sample space?

The 16 outcomes in S are
{F,F,F,F} , {F,F,F,V}, {F,F,V,F}, {F,F,V,V}, {F,V,F,F}, {F,V,F,V}, {F,V,V,F}, {F,V,V,V},
{V,F,F,F} , {V,F,F,V}, {V,F,V,F}, {V,F,V,V}, {V,V,F,F}, {V,V,F,V}, {V,V,V,F}, {V,V,V,V}

b) Which outcomes are in the event that exactly three of the selected mortgages are fixed rates?

The outcomes are in the event that exactly three of the selected mortgages are fixed rates

{(F,F,F,V),(V,F,F,F),(F,V,F,F),(F,F,V,F)
c) Which outcomes are in the event that all four mortgages are of the same type?

The outcomes in the event that all four mortgages are of same type
{F,F,F,F} , {V,V,V,V}

d) Which outcomes are in the event that at most one of the four is a variable-rate mortgage?

The outcomes are in the event that at most one of the four is a variable-rate mortgage

{(F,F,F,F),(F,F,F,V),(F,F,V,F),(F,V,F,F),(V,F,F,F),(V,F,F,F)
e) What is the union of the events in parts (c) and (d), and what is the intersection of these two events?

(c) Union (d) is,
{F,F,F,F} , {F,F,F,V}, {F,F,V,F}, {F,V,F,F}, {V,F,F,F}, {V,V,V,V}

(c) intersection (d) is,
{F,F,F,F}

f) What are the union and intersection of the two events in parts (b) and (c)?

(b) Union (c) is,
{(F,F,F,V),(V,F,F,F),(F,V,F,F),(F,F,V,F),(F,F,F,F),(V,V,V,V)}

(b) intersection (c) is a null set as no elements in (b) and (c) are common