Probability Problem: Defaulting on Payments

• war485
In summary, the probability of defaulting on the nth payment is 0.017n - 0.013 where n is a whole number, and the probability of making all 10 payments is 57.4%. Additionally, the probability of making only the first 5 payments is 56.3%. These probabilities are calculated by multiplying the probabilities of not defaulting on each individual payment, which are independent events. It may be helpful to use a probability tree to visualize the calculations.
war485
Problem:
The probability of defaulting on the nth payment is 0.017n - 0.013 where n is a whole number, n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
find:
1) the probability of making all 10 payments
2) the probability of making only the first 5 payments
Note: each payment made are equal

My idea:

I was thinking that defaulting means I won't make the payment, so
is this the right answer to the first question?
P = ( 1 - (0.017 - 0.013)) * ( 1 - (0.017(2) - 0.013)) * ( 1 - (0.017(3) - 0.013)) * ... * ( 1 - (0.017(10) - 0.013))

and similarly for the second one:
P = P = ( 1 - (0.017 - 0.013)) * ( 1 - (0.017(2) - 0.013)) * ( 1 - (0.017(3) - 0.013)) * ( 1 - (0.017(4) - 0.013)) * ( 1 - (0.017(5) - 0.013))

Does that make sense? Taking the probability for each payment by 1 - failure and then multiply each of them. Am I doing this right? I'm not good at probability yet.

You have the right idea. They are independent events. My TI-86 gets 42.6% possibility of not defaulting on ten payments.

A simple problem is to consider the possibility of test failure to be 1/4 and they are to be three tests. Then the possibiility of passing all tests is (3/4)^3.

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It often helps to draw the probability tree - try this and you might spot the term missing from one of your expressions.

bpet said:
It often helps to draw the probability tree - try this and you might spot the term missing from one of your expressions.

? I checked it over with a tree diagram. How am I missing a term?

(edit): would I have to include the probability of defaulting in the second question? i.e. keep multiplying my answer by (0.017n - 0.013) where n = 6, ... 10 ?

(edit #2): I got it now. Thanks guys!

Last edited:

1. What is a probability problem regarding defaulting on payments?

A probability problem regarding defaulting on payments is a scenario where an individual or organization may not be able to pay back a loan or fulfill a financial obligation on time.

2. What factors affect the probability of defaulting on payments?

Several factors can affect the probability of defaulting on payments, including income, credit score, debt-to-income ratio, and financial stability.

3. How is the probability of defaulting on payments calculated?

The probability of defaulting on payments is calculated by analyzing historical data, risk factors, and financial indicators to determine the likelihood of an individual or organization failing to make payments on time.

4. What are some strategies to reduce the probability of defaulting on payments?

Some strategies to reduce the probability of defaulting on payments include improving credit score, reducing debt, increasing income, and creating a solid financial plan.

5. How can probability problems related to defaulting on payments be used by financial institutions?

Financial institutions can use probability problems related to defaulting on payments to assess risk and make informed decisions about lending money or extending credit to individuals or organizations. This can help them mitigate potential losses and manage their portfolios more effectively.

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