A local public-action group solicits donations by telephone. For a particular list of prospects, it was estimated that for any individual the probability was 0.05 of an immediate donation by credit card, 0.29 of no immediate donation but a request for further information through the mail, and 0.66 of no expression of interest. Information is mailed to all people requesting it, and it is estimated that 30% of these people will eventually donate. An operator makes a sequence of calls, the outcomes of which can be assumed to be independent. What is the probability that the first call leading to any donation (either immediately or eventually after a mailing) is preceded by at least five calls that never lead to a donation? (Round to three decimal places as needed)

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.2: Introduction To Probability
Problem 52E
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A local public-action group solicits donations by telephone. For a particular list of prospects, it was estimated that for any individual
the probability was 0.05 of an immediate donation by credit card, 0.29 of no immediate donation but a request for further
information through the mail, and 0.66 of no expression of interest. Information is mailed to all people requesting it, and it is
estimated that 30% of these people will eventually donate. An operator makes a sequence of calls, the outcomes of which can be
assumed to be independent. What is the probability that the first call leading to any donation (either immediately or eventually after
a mailing) is preceded by at least five calls that never lead to a donation? (Round to three decimal places as needed)
Transcribed Image Text:A local public-action group solicits donations by telephone. For a particular list of prospects, it was estimated that for any individual the probability was 0.05 of an immediate donation by credit card, 0.29 of no immediate donation but a request for further information through the mail, and 0.66 of no expression of interest. Information is mailed to all people requesting it, and it is estimated that 30% of these people will eventually donate. An operator makes a sequence of calls, the outcomes of which can be assumed to be independent. What is the probability that the first call leading to any donation (either immediately or eventually after a mailing) is preceded by at least five calls that never lead to a donation? (Round to three decimal places as needed)
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