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Answer to Question #24543 in Abstract Algebra for pascal

Question #24543
on a given day, each computer in a laboratory has at most one crash. there is 5% chances that the computer has a crash during the day,independent of the performance of any other computer. there are 25 computers in the laboratory. find the probability that on a given day
a.exactly 3 crashes
b.at most 3 crashes
c.at least 3 crashes
d.more than 3 crashes and less than 6
Expert's answer

a -- probability of 3 errors and 22 non-errors
b -- sum of probabilities of 0 crashes and 25 non-crashes WITH (1, 24) WITH
(2,23) WITH (3,22)
c -- probability of event (at least 3 crashes) is equal to probability to
event, reverse to (0 crashes OR 1 crash OR 2 crashes)
d -- sum of probabilities of (4,21), (5,20)

a) (5%)^3 * (1-5%)^22
b) (1-5%)^25 + 5% * (1-5%)^24 + (5%)^2 * (1-5%)^23 + (5%)^3 * (1-5%)^22
c) 1 - ((1-5%)^25 + 5% * (1-5%)^24 + (5%)^2 * (1-5%)^23)
d) (5%)^4 * (1-5%)^21 + (5%)^5 * (1-5%)^20

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