Question

A new computer virus can enter the system through an email or through a webpage. there is a 30\% chance of receiving this virus through the email. there is a 40\% chance of receiving it through the webpage. also, the virus enters the system simultaneously through the email and the webpage with probability 0.15. what is the probability that the virus does not enter the system at all?

Answer 1

In solving this probability problem, you can use the Venn diagram to help you visualize the problem. The Venn diagram makes use of circles with their perimeter acting as the boundaries. Please see the attached picture. 

The left circle stands for the probability of email virus, so it is assigned with 0.3. The right circle stands for the probability of webpage virus, so it is assigned with 0.4. The common area between the circle is probability of email and webpage virus assigned with 0.15. From there, we subtract 0.3 and 0.4 with 0.15 to differentiate which is email alone or which is webpage alone. The x outside the circles is the probability that the virus does not enter the system at all. Since these are probabilities, they add up to 1.

1 = 0.15 + 0.15 +0.25 +x
x = 0.45