1. There are 5 white balls and 4 black balls in a box. We sample without replacement 3 balls. Find the probability of the event A = " among the three balls drawn - there are two white balls and one black ball".
   
   
2. K identical balls have been located randomly in n drawers. What is the probability that in a certain drawer there are h balls?
   
   
3. Let's consider the formula of propositional calculus α = q1 → (q2 → q3). We randomly select a sequence of values for the variables q1, q2, q3. Let's assume that selecting any sequence of three elements is equally probable. What is the probability that the selected sequence (valuation) satisfies the formula α?
   
   
4. There have been n people sampled among the inhabitants of Warsaw, n<365. What is the probability that there are no two people born on the same day?
   
   
5. We roll 6 dice. What is the probability that there are no two dice with the same number of pips?
   
   
6. There are 5 people in the lift of an 8-floor-building. We assume that leaving the lift by a person on a certain floor doesn't depend on the fact of leaving the lift by other people. Find the probability of the events: A = "everybody leaves the lift on the same floor", B=" each person leaves the lift on a different floor".
   
   
7. A student comes for an exam. He knows the answers to 20 questions out of 25. The examiner asks him 3 questions. What is the probability that the student will answer all 3 questions, if the probability of choosing any question is equal?
   
   

 

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