In: Statistics and Probability
a) A country’s sovereign debt is classified according to that country’s capacity to pay its debt as C or high risk (low capacity to pay its debt), B or moderate risk (decent capacity to pay its debt) and A or low risk (high capacity to pay its debt). If for some reason a country is unable to pay its debt then is said to have defaulted. Over the last year out of all the countries that issue debt
• 10% were classified as C
• 30% were classified as B
• The rest were classified as A
• 40% of high risk countries defualted
• 10% of moderate risk countries defualted
• 1% of low risk countries defualted
Given that a country did not defaulted calculate the probability that it was classified as a moderate risk country.
We know the following probabilities
10% were classified as C
The probability that a country is classified as high risk is
• 30% were classified as B
The probability that a country is classified as moderate risk is
• The rest were classified as A
The probability that a country is classified as low risk is
• 40% of high risk countries defualted
The probability of default given that the country is high risk is
• 10% of moderate risk countries defualted
The probability of default given that the country is moderate risk is
• 1% of low risk countries defualted
The probability of default given that the country is low risk is
The probability that any given country defaults is
Given that a country did not default, the probability that it was classified as a moderate risk country is
ans: Given that a country did not default, the probability that it was classified as a moderate risk country is 0.2922