I never knew calculating probability was so difficult!

[maggie2]

I'm having a really hard time wrapping my mind around these questions! I think I might be thinking of this too simplistically. If someone could look over my work and let me know what i'm doing wrong I would really appreciate it.

The STT department has 3 concurrent and independent network servers. The probability of any one of the servers crashing for the day is .14. A full network outage occurs if all 3 servers are down in one day.

a) What is the expected number of outages for N=365 days? My answer is
.14^3=.002744, I multiplied this by 365. My answer is 1 day.

b) What is the variance in the number of outages for N=365 days? I have no idea how to calculate this.

c.) What is the probability of a network outage occuring exactly 2 times per year? I did (.14^3)^2 so .14^6 because I first needed to calculate the probability for one day and then for 2 days?

d) What is the probability of 7 or more network outages in a year. I did this the same way as part c. (.14^3)^7. The answer I calculated is very improbable.

e) what is the probability of 2 or less network outages in a year. I did the probability of the server working in one day squared. .626^2=.404

[jerryb]

parts c, d and e are binomial probabilities with 365 trials probability of a success .14^3 and for part c 2 successes. note that in this example a success is a network outage. i get .184, can you?

for d. use the binomial cumulative distribution for 6 failures and subtract from 1 to get = .000081

for e. again cumulative distibution for 2 or less = .919

cheers
jerry

[maggie2]

I think I get it now. I was thinking I could use regular probability. Instead I used (n/x)*(p)^x*(1-p)^(n-x) where n=365, p=.002744 and x=2. After I did all my calculations I got .17 so I may have a rounding error. I'm just happy to understand what i'm doing a little!

I'm working on the other two parts now.

I also think I figured out how to do the variance now!

Thanks.

[maggie2]

If I have a question that gives the daily failure rate of a server card as .24 and I need to find the probability of 9 network outages. I would use the binomial again?

[jerryb]

You can use binomial probability any time you have repeated trials of an experiment with two mutually exclusive outcomes. in this case your experiment is one day of operation and your outcomes are outage or no outage. if you repeat that experiment, say everyday for a year, then you have a binomial experiment. you will need to know the probability of an outage on a given day so your failure rate of a server card may or may not be the right probability.
cheers
jerry