There is a horrible disease spreading. If you get the disease, it will turn you
ID: 2506224 • Letter: T
Question
There is a horrible disease spreading. If you get the disease, it will turn you into a shrubbery.
There are two different tests for the disease - one tests your blood and the other tests your saliva. The tests
are very rarely in error. You see on the news that the probability that a randomly selected person will test
positive for the first test is 0.2 and the probability that a randomly selected person will test positive for the
second test is also 0.2.
Your friend intends to have both tests done. Knowing that you are an expert in probability, he asks you:
"What is the probability that both tests will turn out positive?"
a. What would the correct answer be if the test results were independent?
b. Do you think that the two test results are actually independent? Explain.
c. Do you think that the right answer to your friend's question is higher or lower than what you guessed
in part a.? Explain in the context of part b.
Explanation / Answer
if the results are independent, probability = 0.2*0.2 = 0.04
In probability theory, to say that two events are independent means that the occurrence of one does not affect the probability of the other. Howevver, in the above case, given that both the tests are very rarely in error, it is highly unlikely that these two tests will be independent. It is very likely that the result of the two tests will be same as the difference of results would imply one of the tests is wrong which is very rare. Hence, the positive result in one of the tests will imply the positive result in other as well.
Probability will be higher, as the probability for a random person selected to be positive is 0.2, and the as explained in part b, both tests being seldom wrong in error will show the same result.
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