Let V be the event that a computer contains a virus, and let W be the event that a computer contains a worm. Suppose P(V)=0.15, P(W)=0.05, and
a. Find the probability that the computer contains both a virus and a worm.
b. Find the probability that the computer contains neither a virus nor a worm.
c. Find the probability that the computer contains a virus but not a worm.
(a) P(V ? W) = P(V) + P(W) ? P(V ?W)
= 0.15 + 0.05 ? 0.17
= 0.03
(b) P(
? 
) = 1?P(V ?W) = 1?0.17 = 0.83.
(c) We need to find P(V ? ). Now P(V) = P(V ? W) + P(V ? )(this can be seen from a Venn diagram). We know that P(V) = 0.15, and from part (a) we know that P(V ? W) = 0.03. Therefore P(V ? ) = 0.12.
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