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\title{
Exam for Probability \& Statistics (6PAS1) \\ winter semester 2025/2026
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\section*{Questions set no. 5}

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\textbf{1.} 
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a) Write a formula for the probability of the union of two arbitrary random events.
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b) What is the relationship between probabilities of an arbitrary random event and its complement? 
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c) Give at least 4 different definitions of independence of two random events.
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d) Give a definition of independence of two random variables.


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\textbf{2.}
Every day in a 30-day month, arrives a shipment with 250 processors, among them
17 are faulty. A controller selects randomly 5 processors. Let $X$ be the number
of faulty processors among those selected by the controller. What is the 
probability that $X = 0$ at least in 50\% of all days?



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