I am helping my brother

nigma

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May 12, 2016
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The Question is as follow:
A computer virus which is known to infect 2% of files has been detected on your system. You have decided to use a virus checker which is 95% reliable when scanning infected files and 99% reliable for files that are not infected.
Consider a file which is marked as infected. Knowing that sometimes the test maybe wrong, what is the probability that the file is indeed infected with the virus?

This is my solution I thought of and need inputs if my logic is wrong anywhere. Since, leaving university since 2011, it seems I have become rusty.

Solution:
So 2% of whole files is infected. 95% of that 2% will be marked by the virus checker.
Which gives me a number 95% * 2%

However, there will be 98% files that are not infected and the virus checker will determine that 99% are infected.
Which gives a number 99% * 98%

Consider a file that is marked as infected which means the first number.
Now sometimes it goes wrong, so there is chance that 5% * 98% is infected too. There is also a chance that there might be 1% * 98% being infected and 5% * 2% not being infected at all.

Which eventually gives the answer of:
{(95% * 2% + 99% * 98%) - ( 5% * 2%)}/ (1% * 98% + 5% * 98%)

Am I correct here??
 
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