A bank classifies borrowers as high risk or low risk. Only...

A bank classifies borrowers as high risk or low risk. Only $15 \%$ of its loans are made to those in the highrisk category. Of all its loans, $5 \%$ are in default, and $40 \%$ of those in default were made to high-risk borrowers. What is the probability that a high-risk borrower will default?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Conditional Probability

Conditional probability is the measure of the likelihood of an event occurring given that another event has already occurred. It is essential for understanding how probabilities change when additional information is provided about the circumstances related to the event of interest.

Bayes' Theorem

Bayes' Theorem is a fundamental principle used to update the probability for a hypothesis as more evidence becomes available. In the context of the problem, it helps reverse conditional probabilities, allowing computation of the likelihood of default for high-risk borrowers based on the probability that a defaulted loan belongs to that group.

Prior Probability

Prior probability refers to the initial assessment of the probability of an event before any additional evidence is taken into account. This baseline measure is crucial in Bayesian analysis, as it represents the starting point for updating beliefs when new data, such as the overall default rate or risk classification statistics, is considered.

Transcript

Please give Ace some feedback