An article in Information Security Technical Report ["Malicious Software Past, Present and Future" (2004, Vol. 9, pp. 6-18)] provided the following data on the top ten mali- cious software instances for 2002. The clear leader in the num- ber of registered incidences for the year 2002 was the Internet worm "Klez," and it is still one of the most widespread threats. This virus was first detected on 26 October 2001, and it has held the top spot among malicious software for the longest period in the history of virology. Place Name % Instances 1 I-Worm Klez 61.22% 2 1-Worm Lentin 20.52% 3 J-Worm Tanatos 2.09% 4 I-Worm Badtransl 1.31% 5 Macro. Word97.This 1.19% 6 I-Worm Hybris 0.60% 7 J-Worm Bridex 0.32% 8 J-Worm Magistr 0.30% 9 Win95.CIH 0.27% 10 J-Worm.Sircam 0.24% The 10 most widespread malicious programs for 2002 (Source-Kaspersky Lab Suppose that 20 malicious software instances are reported. Assume that the malicious sources can be assumed to be inde- pendent.

(a) What is the probability that at least one instance is "Klez"?

(b) What is the probability that three or more instances are "Klez"?

(c) What are the mean and standard deviation of the number of "Klez" instances among the 20 reported?