Suppose 100 people are waiting for blood test for a kind ofdisease. The probibil

Question

Suppose 100 people are waiting for blood test for a kind ofdisease. The probibility that for one person the test resultis positive equals 0.1. Two test methods are as follows: Method 1: Test one by one. Then we have to do 100 tests. Method 2: Divide 100 people into 25 groups with 4 people ineach. Then, mix 4 people's blood and test. If theresult is negative, then everyone in this group is negative. If the result is positive, then we test these 4 people one byone. Now, the number of tests becomes 1+4=5 Question: Which method is better? Suppose 100 people are waiting for blood test for a kind ofdisease. The probibility that for one person the test resultis positive equals 0.1. Two test methods are as follows: Method 1: Test one by one. Then we have to do 100 tests. Method 2: Divide 100 people into 25 groups with 4 people ineach. Then, mix 4 people's blood and test. If theresult is negative, then everyone in this group is negative. If the result is positive, then we test these 4 people one byone. Now, the number of tests becomes 1+4=5 Question: Which method is better?

Explanation / Answer

Since the likely hood that some one will be sick is low (10%) the second method will be better because fewer tests will need to be taken. If 10 sick people (out of 100) are all in different groups then then ten out of twenty five groups will have five instead of one test. So the max number of tests for method two is (5*10)+15=65 total tests. 100 tests for method 1 or 65 tests for method 2. With the same accuracy method two saves money and is faster.

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