Q.#3 (a) In a certain industrial facility, accidents occur infrequently. It is known that the probability of an accident on any given day is 0.005 and accidents are independent of each other. (i) What is the probability that in any given period of 400 days there will be an accident on one day? (ii) What is the probability that there are at most three days with an accident? (iii) Find P(2 < X < 4 /X < 3)

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Q.#3 (a) In a certain industrial facility, accidents occur infrequently. It is known that the probability of an
accident on any given day is 0.005 and accidents are independent of each other.
(i) What is the probability that in any given period of 400 days there will be an accident on one day?
(ii) What is the probability that there are at most three days with an accident?
(iii) Find P(2 < X < 4 /X < 3)
(b) VLSI chips, essential to the running of a computer system, fail in accordance with a Poisson distribution
with the rate of one chip in about 5 weeks, if there are two spare chips on hand, and if a new supply will
arrive in 8 weeks what is the probability that during the next 8 weeks the system will be down for a week
or more, owing a lack of chips?
Transcribed Image Text:Q.#3 (a) In a certain industrial facility, accidents occur infrequently. It is known that the probability of an accident on any given day is 0.005 and accidents are independent of each other. (i) What is the probability that in any given period of 400 days there will be an accident on one day? (ii) What is the probability that there are at most three days with an accident? (iii) Find P(2 < X < 4 /X < 3) (b) VLSI chips, essential to the running of a computer system, fail in accordance with a Poisson distribution with the rate of one chip in about 5 weeks, if there are two spare chips on hand, and if a new supply will arrive in 8 weeks what is the probability that during the next 8 weeks the system will be down for a week or more, owing a lack of chips?
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