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# Problems in the theory of probability and mat.statistike

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**05.04.2012**

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1. Independently 5 people sit in a train containing 13 cars. Find the probability that they will go in different cars.

2. In a batch of 13 pieces has 8 standard. Randomly selected 7 items. Get the probability that among the selected items exactly 5 standard.

3. The kiosk sells lottery tickets 9, of which the number of winning is 3 pieces. Student bought 4 tickets. What is the probability that a winning number among them is not less than 2 but not greater than 3?

8. In the square with sides 15m randomly thrown point. Get the likelihood that this point will be in the right upper quarter of a square or not more than 2 m from the center of the square.

17. Let A and B - the probability of events. Find the smallest possible probability of the event.

22. In the box 8 white and 13 black balls. Two players alternately recovered over the ball, each time returning it back. The winner is the first one to pull out the white ball. What is the probability of winning a game for a beginner?

25. The urn containing 20 balls, dropped the white ball, then recovered a ball at random. Find the probability that the ball will be extracted white if all equally possible assumptions about the initial amount of white balls in the urn.

26. In the first 5 urn white and 3 black balls, the second - 6 white and 9 black. From the second ballot boxes randomly shift in the first two balls, and then take the urn from the first one ball. What is the probability that the ball - white?

30.Imeetsya 13 coins, of which 3 are defective pieces: as a result of factory defects on these coins minted on both sides of the coat of arms. Randomly selected coins are not looking at the drop out 9 time and for all throws up she goes to the arms. Find the probability that the coin was chosen with two coats of arms.

34.Veroyatnost hitting the target in one shot is equal to 0.18. Made of 7 shots. Get the probability that the target hit at least three times.

# Additional information

Total 181 solved the problem for all sections of the theory of probability and mathematical statistics.