GPL Mathematical Skills | Probability

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Q. No. 19:	A medical clinic tests blood for certain disease from which approximately one person in a hundred suffers. people come to the clinic in group of 50. The operator of the clinic wonders whether he can increase the efficiency of the testing procedure by conducting pooled tests. In the pooled test, the operator would pool the 50 blood samples and test them altogether. If the polled test was negative, he could pronounce the whole group healthy. If not, he could then test each person's blood individually. The expected number of tests the operator will have to perform if he pools the blood samples are :
A :	47
B :	25
C :	21
D :	None of these

Solution Answer: C 1 person in 100 person suffer from disease. It means 99% person are healthy. Probability that a person is healthy = 99/100 = 0.99 In a group of 50 people if the test is positive, then we have to perform 50 test individually on each person and 1 group test. So, probability that in a group of 50 people all are healthy => 50_C₅₀(0.99)⁵⁰ = 0.605 So, the probability that in the group of 50 people at least one people suffer => 1- 0.605 = 0.395 Expected number of tests = (51 0.395) + (0.605*1) = 20.75 = 21 test.