# The Probability of Default on A Seven Year AA Rated Bond Question

Problem 1:

An analyst estimates that the probability of default on a seven-year AA-rated bond is 0.06, while that on a seven-year A-rated bond is 0.13. The probability that they will both default is 0.04.

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• What is the probability that at least one of the bonds defaults?
• What is the probability that neither the seven-year AA-rated bond nor the seven-year A-rated bond defaults?
• Given the seven-year AA-rated bond defaults, what is the probability that the seven-year A-rated bond also defaults?
• Problem 2:

Organizers of an outdoor summer concert are concerned about the whether conditions on the day of the concert. They will make a profit of \$25,000 on a clear day and \$10,000 on a cloudy day. They will take a loss of \$5,000 if it rains. The weather channel has predicted a 60% chance of rain on the day of the concert. Calculate the expected profit from the concert if the likelihood is 10% that it will be sunny and 30% that it will be cloudy.

Problem 3:

The average rent in a city is \$1,500 per month with a standard deviation of \$250. Assume rent follows the normal distribution. What percentage of rents are between \$1,250 and \$1,750?

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