SOLUTION: The IT department runs 3 redundant computer servers concurrently. For each server there is a 14% chance of crashing in a given day. Assume that a server crashing is independent f

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Question 31005: The IT department runs 3 redundant computer servers concurrently. For each server there is a 14% chance of crashing in a given day. Assume that a server crashing is independent from any other server crashing.
a) What is the probability that none of the 3 servers will crash for 7 consecutive days.
b) What is the probability that at least one server will crash in a seven day period?
c) What is the probability of a full network outage (all three servers going) in a given day?
I don't even know where to start with this question. Every time I try something the answer seems ridiculous. Any help would be appreciated.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
The IT department runs 3 redundant computer servers concurrently. For each server there is a 14% chance of crashing in a given day. Assume that a server crashing is independent from any other server crashing.
a) What is the probability that none of the 3 servers will crash for 7 consecutive days.
P WORKING FOR 1 SERVER =(100-14)%=86%=0.86
IT IS SAME FOR OTHER 2 SERVERS AND THEY ARE ALL INDEPENDENT.HENCE PROBABILITY THAT ALL 3 WORK ON A DAY =0.86^3=0.636
IT IS SAME FOR EVERY DAY IN A WEEK.HENCE FOR 7 DAYS PROBABILITY OF ALL WORKING =
{(0.86^3)}^7=0.86^21=0.042
b) What is the probability that at least one server will crash in a seven day period?
PROBABILITY THAYT AT LEAST 1 WILL FAIL =1-NONE WILL FAIL =1-0.042=0.958
c) What is the probability of a full network outage (all three servers going) in a given day?
IT IS 0.14*0.14*0.14=0.002744
I don't even know where to start with this question. Every time I try something the answer seems ridiculous. Any help would be appreciated.
You may edit the question. Maybe convert formulae to