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In a residential area, a bike-sharing station serves a group of \(200\) regular commuters. Statistical data shows that on any given morning, the probability that a specific commuter needs to take a bike from this station is \(0.3\). We assume that the commuters' decisions are independent.
The city wants to determine the minimum number of bikes \(k\) that should be docked at the station every morning.
Determine \(k\) such that the probability that every commuter who wants a bike can find one is at least \(95\,\pourcent\).
If the city wants to be more reliable and ensures this probability is at least \(99\,\pourcent\), how many bikes \(k\) must be provided?
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