Upon testing a model used to detect rotten tomatoes, the following data was observed by...

To calculate the accuracy, recall, and specificity from the confusion matrix provided, we use the following formulas:

Confusion Matrix:

Actually Rotten: 45 (True Positive), 8 (False Positive)

Actually Fresh: 5 (False Negative), 42 (True Negative)

Accuracy:

Accuracy is the proportion of true results (both true positives and true negatives) in the total population.

Formula: Accuracy=TP+TNTP+TN+FP+FN\text{Accuracy} = \frac{TP + TN}{TP + TN + FP + FN}Accuracy=TP+TN+FP+FNTP+TN​

Calculation: Accuracy=45+4245+42+8+5=87100=0.87\text{Accuracy} = \frac{45 + 42}{45 + 42 + 8 + 5} = \frac{87}{100} = 0.87Accuracy=45+42+8+545+42​=10087​=0.87

Recall (Sensitivity):

Recall is the proportion of true positive results in the total actual positives.

Formula: Recall=TPTP+FN\text{Recall} = \frac{TP}{TP + FN}Recall=TP+FNTP​

Calculation: Recall=4545+5=4550=0.9\text{Recall} = \frac{45}{45 + 5} = \frac{45}{50} = 0.9Recall=45+545​=5045​=0.9

Specificity:

Specificity is the proportion of true negative results in the total actual negatives.

Formula: Specificity=TNTN+FP\text{Specificity} = \frac{TN}{TN + FP}Specificity=TN+FPTN​

Calculation: Specificity=4242+8=4250=0.84\text{Specificity} = \frac{42}{42 + 8} = \frac{42}{50} = 0.84Specificity=42+842​=5042​=0.84

Therefore, the correct combinations of accuracy, recall, and specificity are 0.87, 0.9, and 0.84 respectively.