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An eco-district has \(120\) electric cars. Each night, the probability that a specific car needs to be plugged into a charging station is \(0.25\). We assume the charging needs of the cars are independent.
The developer wants to install a minimum number of charging points \(k\) to avoid unnecessary costs.
Determine \(k\) such that the probability that all cars needing a charge can find an available station is at least \(95\,\pourcent\).
To increase the "premium" standing of the district, the developer now wants this probability to be at least \(99\,\pourcent\). Determine the new value of \(k\).
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