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, p(v ∪ w) = 0.17. (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.

We have been given that the probability of a computer containing a virus P(v) is 0.15 and probability of computer containing a worm P(w) is 0.05.

We are also told that probability of computer containing either virus or worm is 0.17.

(a) To find out the probability that the computer contains both a virus and a worm we will use probability formula,

Now let us substitute our given values in this formula.

Therefore, probability that that the computer contains both a virus and a worm is 0.03.

(b) To find out the probability that the computer contains neither a virus nor a worm we will subtract the probability of computer containing both virus and worm from 1.

Therefore, probability that the computer contains neither a virus nor a worm is 0.83.

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.