Question

Your computer has been acting very strangely lately, and you suspect that it might have a virus on it. Unfortunately, all 15 of the different virus detection programs you own are outdated. You know that if your computer does have a virus, each of the programs, independently of the others, has a 0.7 chance of believing that your computer as infected, and a 0.3 chance of thinking your computer is fine. On the other hand, if your computer does not have a virus, each program has a 0.9 chance of believing that your computer is fine, and a 0.1 chance of wrongly thinking your computer is infected. Given that your computer has a 0.65 chance of being infected with some virus, and given that you will believe your virus protection programs only if 12 or more of them agree, find the probability that your detection programs will lead you to the right answer.

Answer 1