Statistics and Probability Answers

The stick of the length L is broken in two randomly selected points. With what probability it is possible to make a triangle with its parts?

What is the probability that in a room of n people, at least two have the same birthday?

There are 90 good and 10 defective screws in the box. What is the probability that there are no defective screws among 10 randomly taken screws?

There are n tickets in the lottery, m of them are winning ones. Someone has bought k tickets. What is the probability that at least one of them is lottery loan?

There are n randomly placed books on a shell with the two-volume edition of Jack London among them. Suppose that the different book arrangements are equiprobable. What is the probability that both volumes are located near each other?

Student came to the exam knowing only 24 questions out of 30. If he doesn’t know the answer on a question he gets a second one. Student can pass the exam if he answers at least one question. What is the probability of passing the exam?

The deck of cards (36 pieces) is randomly divided into 2 equal packs. What is the probability that:
a) there will be two aces in each pack;
b) there will be all four aces in one pack;
c) there will be equal amount of red cards in each pack?

There are 10 red and 6 blue buttons in the box. What is the probability that two randomly taken buttons are of the same color?

Consider A, B and C to be an events. What is the sense of the following equations:
a) ABC = A;
b) A+B+C = A?

What is the more likely sum of the numbers when throwing two dices: 9 or 10?