Sally suspects that her computer has a virus. All 11 of her distinct virus detec

Question

Sally suspects that her computer has a virus. All 11 of her distinct virus detection programs are outdated. If her computer does have a virus each program, independently of each other, has a 70% chance of detecting the virus and a 30% chance of stating the computer is virus free. If the computer does not have a virus, each program has a 90% chance of stating the computer is virus free and a 10% chance of stating it is infected. Sally’s computer has a 75% chance of being infected, and she will only trust the virus detection programs stating the computer is infected if the majority state it is infected. Find the probability that Sally’s detection programs will give her the right answer

Explanation / Answer

says is infected given there is a virus

P(I) =.7

she will accept the computer has virus if 6 or more say she has virus

=11C6p(I)^6 p(NI)^5 + 11C7p(I)^7 p(NI)^4 + 11C8p(I)^8 p(NI)^3 + 11C9p(I)^9 p(NI)^2+ 11C10p(I)^10p(NI)^1 +11C11p(I)^11 p(NI)^0

=0.7896954

now she will say that her computer is infected with ~0.7896954

we need to find P(V | I) = P(I and V) / P(I) =  .75 / 0.7896954 = 0.9497333

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