A medical AI model is used to detect a disease in 500 patients:

100 patients actually have the disease
The model correctly identifies 70 of them
It incorrectly identifies 50 healthy patients as having the disease

Questions:

Calculate the precision of the model.
Calculate the recall of the model.

Question

A medical AI model is used to detect a disease in 500 patients:

100 patients actually have the disease
The model correctly identifies 70 of them
It incorrectly identifies 50 healthy patients as having the disease

Questions:

Calculate the precision of the model.
Calculate the recall of the model.

BlackTom AI · Accepted Answer

Precision measures the proportion of predicted positives that are actually positive: precision = TP / (TP + FP). Recall measures the proportion of actual positives that are correctly identified: recall = TP / (TP + FN).

Relevant knowledge points:
- True Positive (TP): diseased patients correctly identified = 70.
- False Positive (FP): healthy patients incorrectly identified as diseased = 50.
- False Negative (FN): diseased patients the model missed = actual diseased − TP = 100 − 70 = 30.
- True Negative (TN) is not needed for precision/recall but equals total healthy − FP = 400 − 50 = 350.

Step-by-step calculations with intermediate steps:
1. Precision = TP / (TP + FP)
   = 70 / (70 + 50)
   = 70 / 120
   = 0.583333...
   Rounded to two decimal places = 0.58.

2. Recall = TP / (TP + FN)
   = 70 / (70 + 30)
   = 70 / 100
   = 0.7.

Why the correct answer is correct:
- Precision = 0.5833… ≈ 0.58, because out of 120 patients labeled positive by the model (70 true + 50 false), 70 were true positives.
- Recall = 0.7, because the model found 70 of the 100 actual diseased patients.

Why the other options are incorrect:
- Option "0.58, 0.58": precision is correct but recall is wrong (should be 0.70).
- Option "0.7, 0.6": values are incorrect and swapped; precision is not 0.7 and recall is not 0.6.
- Option "0.48, 0.6": neither precision nor recall match the calculated values.

Conclusion: The precision is 0.58 and the recall is 0.7, matching the provided correct answer "0.58, 0.7".

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