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8. An entrant firm may make a technological discovery giving them a product that places strong competition on some rival firm who is already in the marketplace. If they don't make such a discovery, then the only product that the entrant could potentially bring to market is a weak product. Nature determines whether or not the entrant is "strong" or "weak." The entrant knows its own type, and a strong entrant is 80% likely to challenge the incumbent firm, while a weak entrant is only 65% likely to challenge the incumbent. There is a 3/4 chance the entrant is strong. a) Compute prob(challenge). That is, compute the unconditional probability that the entrant challenges. b) Compute prob(don't challenge weak). That is, compute the probability that the entrant doesn't challenge, conditional on the entrant being weak. c) Is the event "the entrant challenges" statistically independent from the event "the entrant is strong?" Explain why or why not.

8. An entrant firm may make a technological discovery giving them a product that places strong competition on some rival firm who is already in the marketplace. If they don't make such a discovery, then the only product that the entrant could potentially bring to market is a weak product. Nature determines whether or not the entrant is "strong" or "weak." The entrant knows its own type, and a strong entrant is 80% likely to challenge the incumbent firm, while a weak entrant is only 65% likely to challenge the incumbent. There is a 3/4 chance the entrant is strong. a) Compute prob(challenge). That is, compute the unconditional probability that the entrant challenges. b) Compute prob(don't challenge weak). That is, compute the probability that the entrant doesn't challenge, conditional on the entrant being weak. c) Is the event "the entrant challenges" statistically independent from the event "the entrant is strong?" Explain why or why not.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 28PPS
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8. An entrant firm may make a technological discovery giving them a product that places strong competition on some rival firm who is already in the marketplace. If they don't make such a discovery, then the only product that the entrant could potentially bring to market is a weak product. Nature determines whether or not the entrant is "strong" or "weak." The entrant knows its own type, and a strong entrant is 80% likely to challenge the incumbent firm, while a weak entrant is only 65% likely to challenge the incumbent. There is a 3/4 chance the entrant is strong. a) Compute prob(challenge). That is, compute the unconditional probability that the entrant challenges. b) Compute prob(don't challenge weak). That is, compute the probability that the entrant doesn't challenge, conditional on the entrant being weak. c) Is the event "the entrant challenges" statistically independent from the event "the entrant is strong?" Explain why or why not.
Transcribed Image Text:8. An entrant firm may make a technological discovery giving them a product that places strong competition on some rival firm who is already in the marketplace. If they don't make such a discovery, then the only product that the entrant could potentially bring to market is a weak product. Nature determines whether or not the entrant is "strong" or "weak." The entrant knows its own type, and a strong entrant is 80% likely to challenge the incumbent firm, while a weak entrant is only 65% likely to challenge the incumbent. There is a 3/4 chance the entrant is strong. a) Compute prob(challenge). That is, compute the unconditional probability that the entrant challenges. b) Compute prob(don't challenge weak). That is, compute the probability that the entrant doesn't challenge, conditional on the entrant being weak. c) Is the event "the entrant challenges" statistically independent from the event "the entrant is strong?" Explain why or why not.
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