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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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?

Gene
4.5
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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