K 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 0.07 of default. (a) What is the probability that a randomly selected mortgage will not default? (b) What is the probability that nine 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 nine 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 0.93 (Type an integer or a decimal. Do not round.) (b) The probability is 0.5204 (Round to four decimal places as needed.) (c) The probability is (Round to four decimal places as needed.) ▪▪▪

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...
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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 0.07 of default.
(a) What is the probability that a randomly selected mortgage will not default?
(b) What is the probability that nine 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 nine 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 0.93
(Type an integer or a decimal. Do not round.)
(b) The probability is 0.5204
(Round to four decimal places as needed.)
(c) The probability is
(Round to four decimal places as needed.)
.…
Transcribed Image Text:K 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 0.07 of default. (a) What is the probability that a randomly selected mortgage will not default? (b) What is the probability that nine 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 nine 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 0.93 (Type an integer or a decimal. Do not round.) (b) The probability is 0.5204 (Round to four decimal places as needed.) (c) The probability is (Round to four decimal places as needed.) .…
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