write me a problem statement with answer on evaluation accuracy rate

Problem Statement:

In the field of machine learning, the accuracy rate of a model is a crucial metric for evaluating its performance. This is particularly true for classification problems, where the accuracy rate is defined as the proportion of true results (both true positives and true negatives) in the population.

A company has developed a new algorithm for detecting fraudulent transactions. They have tested this algorithm on a dataset of 10,000 transactions, which includes 100 fraudulent transactions. The algorithm correctly identified 90 of the fraudulent transactions, but also flagged 200 legitimate transactions as fraudulent.

The problem is to evaluate the accuracy rate of this algorithm.

Solution:

Step 1: Calculate the number of true positives (TP): This is the number of fraudulent transactions the algorithm correctly identified, which is 90.

Step 2: Calculate the number of true negatives (TN): This is the number of legitimate transactions the algorithm correctly identified. Since there were 200 legitimate transactions flagged as fraudulent, the number of true negatives is 10,000 - 100 (total transactions - fraudulent transactions) - 200 (legitimate transactions flagged as fraudulent) = 9,700.

Step 3: Calculate the accuracy rate: The accuracy rate is calculated as (TP + TN) / (total number of transactions). So, the accuracy rate is (90 + 9,700) / 10,000 = 0.979 or 97.9%.

Therefore, the accuracy rate of the algorithm is 97.9%.