Practice problems for general probability
P(A | B)
P(A and B)
; P(A or B)= P(A)+ P(B) - P(A and B)
P(B)
1. A new Autopilot system fails to operate successfully .01 % of the time. Its back-up
system fails 10 percent of the time. If the systems operate independently, what is the
probability that both will fail? What is the probability that at least one will fail?
2. A new Autopilot system fails to operate successfully .01 % of the time. Both the
autopilot and its back-up system will fail .001 percent of the time. What is the
probability that the back-up will fail given that the new autopilot failed? If the probability
that the back-up system will fail is 1%, are the systems independent?
3. Twenty percent of WCU students withdraw from ECO 251. Of those withdrawing
from ECO 251, five percent withdraw from the University. What is the probability that a
student will withdraw from the university and Eco 251? Are these events independent?
Explain why or why not.
4. On any given day, .5 percent of the computers in the labs are infected with a virus,
but 95 percent of the viruses are harmless (non-destructive). If a student claims that a
virus destroyed their research paper, should I believe them? Explain why or why not.
If two people (in separate classes with separate projects) had the same "destructive
virus" excuse, is it likely that they are both telling the truth? Explain your answer.
5. McAfee has a virus program that it claims will eliminate 90 percent of all viruses on
your computer. Norton has a program that will eliminate 80 percent of all viruses;
however, the Norton program is sometimes successful when the Mcafee program is
not. Norton will eliminate 50 percent of the viruses that Mcafee misses. If you want
to eliminate 95 percent of the viruses, will running both programs be sufficient?