To find the probability of selecting a subject who is not diabetic given that the test result is negative, we need to use the concept of conditional probability. We are given a table with information about diabetic and non-diabetic subjects and their test results.
The data table shows:
- 3 diabetic subjects with a negative test result.
- 28 not diabetic subjects with a negative test result.
- Total number of subjects with a negative test result = 3 (diabetic) + 28 (not diabetic).
Let's denote:
- [tex]\( A = \text{Subject is not diabetic} \)[/tex]
- [tex]\( B = \text{Test result is negative} \)[/tex]
We are looking for [tex]\( P(A|B) \)[/tex], the probability that a subject is not diabetic given that their test result is negative. This can be found using the formula for conditional probability:
[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \][/tex]
Where:
- [tex]\( P(A \cap B) \)[/tex] is the probability that a subject is not diabetic and has a negative test result.
- [tex]\( P(B) \)[/tex] is the probability that a subject has a negative test result.
From the data:
- [tex]\( P(A \cap B) \)[/tex] is represented by the number of not diabetic subjects with a negative test result, which is 28.
- [tex]\( P(B) \)[/tex] is represented by the total number of subjects with a negative test result, which is 3 (diabetic) + 28 (not diabetic) = 31.
Now, we calculate the probability:
[tex]\[ P(A|B) = \frac{28}{31} \][/tex]
To convert this fraction into a decimal:
[tex]\[ \frac{28}{31} \approx 0.9032258064516129 \][/tex]
Thus, the probability that a randomly selected subject is not diabetic given that their test result is negative is approximately 0.90.
The correct answer is:
D. 0.90
