A trading company has 10 computers that it uses to trade on the New York Stock E

Question

A trading company has 10 computers that it uses to trade on the New York Stock Exchange. The probability of a computer failing in a day is 0.003 and the computers fail independently. Computers are repaired in the evening and each day is an independent trial.

a. What is the probability that exactly 3 computers fail in a day?

b. What is the probability that a week (7 days) passes till the event that exactly 3 computers fail in the same day occurs? [Hint: consider the probability of exactly 3 computers failing in a day (the same day) as a single probability of success]

c. What is the mean number of days until all ten computers fail in the same day?

Explanation / Answer

n = 10

P = 0.003

A) P(X = 3) = 10C3 * (0.003)^3 * (0.997)^7 = 0.0000032

B) Probability = 7 * 0.0000032 = 0.0000224

C) mean = n * P

= 10 * 0.003

= 0.03

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