# Sensitivity of a diagnostic test

#### Mia30

##### New Member
There is an exercise that I am not able to solve: Diagnostic tests A1 and A2 are used to detect the presence or absence of a disease. The results of A1 and A2 are a priori independent of the presence or absence of the disease. A1 and A2 have sensitivity Sen1 and Sen2, respectively. A new diagnostic test T is introduced. T is positive when A1 and A2 are both positive. Determine the sensitivity of T.

Initially, I thought I would use Bayes theorem, as it contains sensitivity and re-arranging the equation I would get the sensitvity of T: P(Test+│D)=P(D│Test+)*(P(test+│D)*P(D)+P(test+│notD)*P(notD))/P(D)

But since there are no numbers behind, I don´t know how to solve this problem..

any help is highly appreciated!

#### katxt

##### Member
The "numbers" are Sen1 and Sen2.
I suspect that you are overthinking the problem.
The sensitivity of T is the probability of a positive given that the patient has the disease and T is positive when A1 and A2 are both positive. So, what is the probability that A1 and A2 will both be positive given that the patient has the disease?

#### Mia30

##### New Member
Thank you Katxt! I indeed have! you just put me on the right track, thanks so much!