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the covid test performed best eight days after infection but even then had a false negative rate of 20 meaning 20 in 100 p

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The Covid test performed best eight days after infection, but even then, had a false negative rate of 20%, meaning 20 in 100 people who truly have Covid - had a negative test result. A friend called you and told you that he has Covid. You met 8 days ago. Your Covid test was negative, but you decided to do one more test-just in case. The second test was also negative. What are the chances that both tests performed on 8th day after exposure to infection were false negative?

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Answer to a math question The Covid test performed best eight days after infection, but even then, had a false negative rate of 20%, meaning 20 in 100 people who truly have Covid - had a negative test result. A friend called you and told you that he has Covid. You met 8 days ago. Your Covid test was negative, but you decided to do one more test-just in case. The second test was also negative. What are the chances that both tests performed on 8th day after exposure to infection were false negative?

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Let's denote the event of having a false negative result on the first test as $F_1$ and the event of having a false negative result on the second test as $F_2$.

We are given that the probability of a false negative result on each test is 20% or 0.20. Since the tests are independent, the probability of both tests giving a false negative result is $P(F_1 \cap F_2) = P(F_1) \cdot P(F_2)$.

Therefore, the probability that both tests are false negative is:

P(F_1 \cap F_2) = 0.20 \cdot 0.20 = 0.04 = \boxed{4\%}

\textbf{Answer:} The chances that both tests performed on the 8th day after exposure to the infection were false negatives are 4%.

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