The state medical school has discovered a new test or tuberculosis. If the test

Question

The state medical school has discovered a new test or tuberculosis. If the test indicates a person has tuberculosis, the test is positive. Experimentation has shown that the probability o a positve test is 0.75, given that a person has tuberculosis. The probability is 0.06 that the test registers positive, given that the person docs not have tuberculosis, Assume that in the general population, the probability that a person has tuberculosis is 0.06, What is the probability that person chosen at rardorn will fall in the following tegories. Enter your answers to our decimal places. (a) have tuberculosis and have a positive test (b) not have tuberculosis (c) not have tuberculosis and have positive test

Explanation / Answer

Here we are given that:

P( TB) = 0.06, P( positive | TB) = 0.75 and P( positive | no TB ) = 0.06

a) Probability that the person has TB and test positive is computed using the Bayes theorem as:

P( TB and positive ) = P( positive | TB) P( TB) = 0.75*0.06 = 0.045

Therefore 0.045 is the required probability here.

b) P( no TB) = 1 - P(TB ) = 1 - 0.06 = 0.94

Therefore 0.94 is the required probability here.

c) P( no TB and positive )

Again using bayes theorem, we get:

P( no TB and positive ) = P( positive | no TB )P( no TB) = 0.06*0.94 = 0.0564

Therefore the required probability here is 0.0564

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.