PRMIA 8010 Exam - Topic 9 Question 76 Discussion

Actual exam question for PRMIA's 8010 exam

Question #: 76
Topic #: 9

[All 8010 Questions]

A Bank Holding Company (BHC) is invested in an investment bank and a retail bank. The BHC defaults for certain if either the investment bank or the retail bank defaults. However, the BHC can also default on its own without either the investment bank or the retail bank defaulting. The investment bank and the retail bank's defaults are independent of each other, with a probability of default of 0.05 each. The BHC's probability of default is 0.11.

What is the probability of default of both the BHC and the investment bank? What is the probability of the BHC's default provided both the investment bank and the retail bank survive?

A0.0475 and 0.10

B0.11 and 0

C0.08 and 0.0475

D0.05 and 0.0125

Show Suggested Answer

Suggested Answer: D

Since the BHC always fails when the investment bank fails, the joint probability of default of the two is merely the probability of the investment bank failing, ie 0.05.

The probability of just the BHC failing, given that both the investment bank and the retail bank have survived will be equal to 0.11 - (0.05+0.05-0.05*0.05) = 0.0125. (The easiest way to understand this would be to consider a venn diagram, where the area under the largest circle is 0.11, and there are two intersecting circles inside this larger circle, each with an area of 0.05 and their intersection accounting for 0.05*0.05. We need to calculate the area outside of the two smaller circles, but within the larger circle representing the BHC).

Refer diagram below, please excuse the awful colors.

by Roosevelt at Aug 12, 2025, 10:49 AM

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Serita

2 months ago

Is the BHC's default really that high compared to the banks?

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Farrah

2 months ago

I’m leaning towards option C, but I’m not entirely sure.

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Sunny

2 months ago

Wait, how can the BHC default without either bank defaulting?

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Lindsey

3 months ago

I think option A makes the most sense here.

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Ahmed

3 months ago

The BHC defaults if either bank defaults, right?

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Katina

3 months ago

I feel like the answer might be option A, but I’m not completely confident. I think we did a problem where we had to find the probability of one event given another, and it was tricky!

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Leigha

3 months ago

If I remember correctly, the probability of both the BHC and the investment bank defaulting should be calculated using the BHC's default probability and the investment bank's.

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Leigha

4 months ago

I'm a bit unsure about how to approach the second part. I think it might involve conditional probability, but I can't recall the exact formula we used.

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Lindsay

4 months ago

I remember we practiced a similar question about independent events and their probabilities. I think the first part involves multiplying the probabilities.

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Cathern

4 months ago

This seems straightforward enough. I just need to apply the right probability formulas based on the independence and dependence relationships described. I'm feeling confident I can get the right answers here.

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Danica

4 months ago

I've got a strategy for this. First, I'll calculate the probability of the BHC and investment bank both defaulting. Then I'll find the probability of the BHC defaulting given the investment and retail banks survive. I think I can do this!

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Dick

4 months ago

Whoa, this is a lot of information to process. I'm a bit confused on how to approach this. Maybe I should start by writing out the given probabilities.

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Kendra

4 months ago

Okay, let's see. The key is understanding the relationship between the BHC, investment bank, and retail bank defaults. I think I can work this out step-by-step.

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Kasandra

5 months ago

Hmm, this looks like a tricky probability question. I'll need to think through the dependencies carefully to get the right answers.

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