Are sensitivity and specificity complement of each other? 
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*Sensitivity : probability that a person with the condition will be classified in one's study as having the condition.

*Specificity : probability that a person without the condition will be classified in one's study as being without the condition.
Are sensitivity and specificity complement of each other ?
But I never found any example where if the sensitivity is $1$, then specificity is $0$.
That means, they are never complement of each other.


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*In probability , the Complement of an event is all outcomes that are NOT the event.


If a diseased person is truly identified as diseased , then s/he will never be classified as non-diseased.
Like, in a dice when the event is ${\{5,6}\}$, the complement is ${\{1,2,3,4\}}$.
I can't establish a clear vision in favor of being their complement or not, i.e., why are sensitivity and specificity complement or not ?
 A: I hope this is not the last answer to this great question, but let me at least fuel the conversation...
You can look at it from the point of view of common denominators: Sensitivity is the number of positive results among patients who are indeed sick, or the probability of a positive test among diseased individuals: p (+ | D), whereas Specificity is the probability of getting a negative result among healthy individuals p( - | H). They have different denominators, hence you can't really add them up to get to 1; or probably better, you are conditioning (Bayes) against two different events (D versus H), making test + not complementary to test - under this condition.
Sensitivity is complementary to False Negative Rate (p( - | D)).
Specificity is complementary to False Positive Rate (p( + | H))
A: As my master said : specificity  and sensitivity are not complement of each other , but we should say that specificity is a complement for false positive and sensitivity is a complement for false negative
