I've been working on my homework for a while, but I got stuck with this question:
A trading company has nine computers that are used to trade on the New York Stock Exchange. The probability of a computer failing in a day is 0.04 and the computers fail independently. Computers are repaired in the evening and each day is an independent trial.
(a) What is the probability that seven computers fail in a day?
(b) What is the mean number of days until a specific computer fails?
(c) What is the mean number of days until seven computers fail in the same day?
I don't understand, how can I tell which distribution to employ. From what I understand I can model (a) as a Binomial Distribution, but in (b) and (c); I don't really get it. What distribution to be used? What is meant by "Mean number of 'days'? and what is meant by 'specific'. And is there is a general method or advice on how to approach such problems?
Thanks.
Some hints:
a) Here you indeed need a binomial distribution.
b) Note that the computer has 0.04 chance to fail every day. So the probability of the number of days till failure follows a geometric distribution.
c) Here you cannot use a common distribution, but you can use the independence of the seven computers.