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Question solve by the hyper geometric distribution method .
Five of 10 new building in a city violate the building code . a random sample of three buildings selected for inspection.
1) what is the probability of none of the building violate the building code in a sample of 3 building .
2) what is the probability of at least one of the new building violate the building code in a sample of 3 building?
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These two statements are the key input information
"Five of 10 new building in a city violate the building code .
a random sample of three buildings selected for inspection."
But there is no any logic connection between these two sentences.
Therefore, the given post, as it is worded, printed and presented, can not be considered as a Math problem.
What buildings are selected for inspection ?
It is UNCLEAR from the post.
To become a Math problem, this text must be edited and re-written.
But it is not my duty to edit it for you.
In opposite, it is YOUR DUTY to present Math problem clearly and properly.