Answer:
a) 3.906 × 10⁻¹⁹
b) 200 days
c) 2.56 × 10¹⁸ days
Step-by-step explanation:
Probability that a computer fails in a day = 0.005.
This probability is very similar to the number of computers that'll fail in a day, that is, number of computer failures per day = 0.005
a) Probability that all the 8 computers fail in a day.
This probability is setup as a binomial distribution problem, but ⁸C₈ = 1 and q⁰ = 1
So, P(X=8) = (0.005)⁸ = 3.906 × 10¹⁹
b) The mean number of days until a specific computer fails
Number of failure = 0.005 per day
Mean number of days = E(X) = 1/0.005 = 200 days
c) Mean number of days until all the 8 computers fail
E(X) = 1/(3.906 × 10⁻¹⁹)
E(X) = 2.56 × 10¹⁸ days
