Question

Let V be the event that a computer contains a virus, and let W be the event that a computer contains a worm. Suppose that P(V)=0.17, P(W)=0.15, and P(V and W)=0.06. Find the probability that the computer contains neither a virus nor a worm.

Report your answer as 0.XX, that is to 2 decimal places.

Your Answer:

Answer 1

The probability that a computer contains neither a virus nor a worm is found by subtracting the probability of the computer containing a virus or a worm from 1, which results in a probability of 0.74.

Step-by-step explanation:

To find the probability that the computer contains neither a virus nor a worm, we can use the formula for the probability of the complement of an event. The complement of the event that a computer contains either a virus or a worm is the event that the computer contains neither a virus nor a worm. So, we can calculate the probability as:

P(neither V nor W) = 1 - P(V or W)

Since P(V and W) = 0.06, we can use the formula:

P(V or W) = P(V) + P(W) - P(V and W)

Substituting the given values, we have:

P(V or W) = 0.17 + 0.15 - 0.06

= 0.26

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

P(neither V nor W) = 1 - 0.26

= 0.74