Question

An ab network consisting of 20 computers was attacked by a computer virus. This virus enters each computer with a probability of 0.4, independently of other computers. Find the probability that at least one computer is infected by the virus?

1) 0.4
2) 0.6
3) 0.8
4) 0.9

Answer 1

To calculate the probability that at least one computer is infected in a network of 20 computers with each having a 0.4 chance of being infected, subtract the probability of no computers being infected (which is 0.6 to the power of 20) from 1.

Step-by-step explanation:

The question is asking for the probability that at least one out of 20 computers in an ab network is infected by a virus when each has a probability of 0.4 of being infected, independently of the others. To find the probability that at least one computer is infected, it's easier to calculate the complement probability—that is, the probability that no computer is infected—and subtract this from 1.

The probability that a single computer is not infected is 1 - 0.4 = 0.6. As the computers are infected independently, the probability that none of the 20 computers are infected is 0.620. Therefore, the probability that at least one computer is infected is 1 - 0.620.

Step-by-step:

1. Calculate the probability that one computer is not infected: 0.6.
2. Compute the probability that none of 20 computers are infected: 0.620.
3. Subtract this probability from 1 to find the probability that at least one computer is infected: 1 - 0.620.