Question

The probability of getting a certain disease is 0.2. A certain test is available which returns a positive result 90% of the time for those with the disease, and a negative result 75% of the time for those without the disease. Compute Pr{Test positive}. (Hint: It may be helpful to draw a probability tree, and round to two decimal plac

Answer 1

Answer:  Pr(test positive ) = 0.38.

Step-by-step explanation:

Since we have given that

Probability of getting a certain disease = 0.2

Probability of not getting a certain disease = 1-0.2 = 0.8

Probability that test turns a positive results for those with the disease = 90% = 0.90

Probability that turns a negative results for those without diseases = 75% = 0.75

Probability that turns a positive results for those without diseases = 1-0.75=0.25

So, Probability of test positive is given by

P(having diseases) . P(test positive) + P(not having diseases) . P(test positive)

$=0.2\times 0.9+0.8\times 0.25\\\\=0.18+0.20\\\\=0.38$

Hence, Pr(test positive ) = 0.38.