Which year did the low profit figure come from?

Applying Bayes' theorem to conditional probability with categorical data

This is an easy probability question that tests your ability to apply Bayes' theorem in a practical, data-driven context. You are given a table of profit figures across sectors and years, observe one data point that satisfies a condition, and must compute the probability of a specific cause. This type of reasoning underpins risk assessment and hypothesis testing in quantitative finance.

To solve problems like this, you identify which outcomes in your sample space satisfy the observed condition, count how many of those outcomes point to each possible source, and weight them proportionally. The key is careful enumeration: listing all figures, filtering by the constraint, and then computing the conditional probability. No advanced distribution theory is required, but precision in accounting for each case is essential.

• Conditional probability and the definition P(A|B) = P(A and B) / P(B)
• Counting and enumeration in finite sample spaces
• Bayes' theorem and reasoning about causes given evidence