Question

In finance, one example of a derivative is a financial asset whose value is determined (derived) from a bundle of various assets, such as mortgages. Suppose a randomly selected mortgage in a certain bundle has a probability of 0.01 of default. (a) What is the probability that a randomly selected mortgage will not default? (b) What is the probability that seven randomly selected mortgages will not default assuming the likelihood any one mortgage being paid off is independent of the others? Note: A derivative might be an investment that only pays when all seven mortgages do not default. (c) What is the probability that the derivative from part (b) becomes worthless? That is, at least one of the mortgages defaults. (a) The probability is (Type an integer or a decimal. Do not round.) (b) The probability is (Round to four decimal places as needed.) (c) The probability is (Round to four decimal places as needed.)

Answer 1

Answer:

Given,

p = 0.01

a)

To give the probability that a randomly selected mortgage will not default

= 1 - 0.01

= 0.99

b)

To give the required probability

P(X= 7) = 7C7*0.99^7*0.01^0

= 0.99^7

= 0.9321

c)

P(X >= 1)

= 1 - 0.99^7

= 1 - 0.9321

= 0.0679