Each of a sample of four home mortgages is classified as fix

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)?

Solution

a)

{FFFF, FFFV, FFVF, FVFF, VFFF, FFVV, FVFV, VFFV, VVFF, VFVF, FVVF, VVVF, VVFV, VFVV, FVVV, VVVV}

b)

{FFFV, FFVF, FVFF, VFFF}

c)

{FFFF, VVVV}

d)

{FFFF, FFFV, FFVF, FVFF, VFFF}

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