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During a financial panic, it is learned that Bank A has a 0.4 chance of collapsing in the next month and that, independently, Bank B has a 0.3 chance of failing. Bank C, which has heavy deposits in both A and B, has a 0.5 probability of failing if one of those banks collapses and a 0.7 chance if both of them fall apart. Otherwise, Bank C will stay afloat. (a) List the eight possible outcomes of the panic (with respect to the fates of the three banks). (b) Find the probability of each of the events identified in (a). What is the probability that all three banks survive the panic?

During a financial panic, it is learned that Bank A has a 0.4 chance of collapsing in the next month and that, independently, Bank B has a 0.3 chance of failing. Bank C, which has heavy deposits in both A and B, has a 0.5 probability of failing if one of those banks collapses and a 0.7 chance if both of them fall apart. Otherwise, Bank C will stay afloat. (a) List the eight possible outcomes of the panic (with respect to the fates of the three banks). (b) Find the probability of each of the events identified in (a). What is the probability that all three banks survive the panic?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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During a financial panic, it is learned that Bank A has a 0.4 chance of collapsing in the next month and that, independently, Bank B has a 0.3 chance of failing. Bank C, which has heavy deposits in both A and B, has a 0.5 probability of failing if one of those banks collapses and a 0.7 chance if both of them fall apart. Otherwise, Bank C will stay afloat. (a) List the eight possible outcomes of the panic (with respect to the fates of the three banks). (b) Find the probability of each of the events identified in (a). What is the probability that all three banks survive the panic?
Transcribed Image Text:During a financial panic, it is learned that Bank A has a 0.4 chance of collapsing in the next month and that, independently, Bank B has a 0.3 chance of failing. Bank C, which has heavy deposits in both A and B, has a 0.5 probability of failing if one of those banks collapses and a 0.7 chance if both of them fall apart. Otherwise, Bank C will stay afloat. (a) List the eight possible outcomes of the panic (with respect to the fates of the three banks). (b) Find the probability of each of the events identified in (a). What is the probability that all three banks survive the panic?
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