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A randomly chosen group is tested for a disease. Within this group, each individual has a probability of 0.1 of having the disease. A test is performed to identify the individuals with the disease. The test has two outcomes: positive or negative. If the individual does not have the disease, the test outcome is “negative” 90 percent of the time. If the individual has the disease, the test outcome is “negative” 20 percent of the time. Individuals who test “positive” are sent to a hospital for further treatment. What is the probability that an individual sent to the hospital indeed has the disease? pls help me with this.

A randomly chosen group is tested for a disease. Within this group, each individual has a probability of 0.1 of having the disease. A test is performed to identify the individuals with the disease. The test has two outcomes: positive or negative. If the individual does not have the disease, the test outcome is “negative” 90 percent of the time. If the individual has the disease, the test outcome is “negative” 20 percent of the time. Individuals who test “positive” are sent to a hospital for further treatment. What is the probability that an individual sent to the hospital indeed has the disease? 
 
pls help me with this.

Grade:12th pass

1 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
the probabilityof a person having the disease is ------ 0.1
the probabilityof a person not having the disease is ------ 0.9

having the disease and testing positive ------ 0.1*0.8
having the disease and not testing positive ------ 0.1*0.2
not having the disease and testing positive ------ 0.9*0.1
not having the disease and not testing positive ------ 0.9*0.9

P(disease)/ P(sent to hospital) = (0.1*0.8)/((0.1*0.8)+(0.9*0.1))
=(0.08)/(0.17)= 8/17 =0.4705

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