GATE 2020 BT Q.54: solution and answer

Official answer: 83.30 to 83.40Source: Official answer key, GATE 2020 BT (IIT Delhi)

1. Step 1 — Identify the sensitivity formula. Sensitivity (also called recall or the true positive rate) is defined as: $$\text{Sensitivity}=\frac{\text{True Positives (TP)}}{\text{Total Actual Positives}}\times 100\%$$ where "Total Actual Positives" is the number of real positive cases that exist in the dataset being searched — not the number the algorithm happened to flag.

2. Step 2 — Identify the values from the question. The database actually contains 78 globin sequences in total — this is the ground-truth positive count. The algorithm retrieved 72 sequences, but only 65 of those retrieved sequences were true globins. So the true positives, TP = 65, and the total actual positives = 78.

3. Step 3 — Apply the formula. $$\text{Sensitivity}=\frac{65}{78}\times 100\%$$

4. Step 4 — Compute and round. $$\frac{65}{78}=0.833333\dots$$ $$0.833333\dots \times 100=83.3333\dots \%$$ Rounded to 2 decimal places: $$\text{Sensitivity}=83.33\%$$