We suppose that $10\%$ of population has been diagnosed by a virus according to a test. Among them $60\%$ has indeed the virus (the test is correct) but among them who has not been diagnosed the percentage that they have been diagnosed is $20\%$ (the test is wrong).
Which is the truth percentage of the test?
We have to use here the conditional probability, or not?
Do we have to calculate $P(\text{truly diagnosed}\mid \text{diagnosed by test})$ ?
Assume there are $1000$ people in total. Now set up the following table: $$\begin{array} {c|c|c} & \text{Positive test} & \text{Negative test} \\ \hline \text{Sick} & & \\ \hline \text{Healthy} & & \\ \end{array}$$
Therefore, there are $100$ people who test positive. $60$ of them have the virus, and $40$ of them do not.
Now fill in the remaining boxes in the same way. You should get:
$$\begin{array} {c|c|c} & \text{Positive test} & \text{Negative test} \\ \hline \text{Sick} & 60 & 180 \\ \hline \text{Healthy} & 40 & 720 \\ \end{array}$$
and from here you can find the accuracy rate of the test.