Task 21. From the group of students, in which 18 boys and 12 girls, two people are elected to the faculty council. What is the likelihood that there will be at least one young man among the elect?

Task 22. The studio has three television cameras. The probability that each camera is turned on at the moment is 0.7. Find the probability that at least one camera is currently turned on.

Task 23. For market research it is necessary to conduct interviews with people who get to work by public transport. In the study area, 75% of people get to work by public transport. If three people agree to be interviewed, then what is the likelihood that at least one of them gets to work by public transport

Task 24. A street vendor offers an illustrated book to passers-by. From previous experience, he knows that on average one of the 50 passers-by to whom he offers a book buys it. Over a period of time, he offered the book to 10 passers-by. What is the likelihood that he will sell them at least one book? Comment on the assumptions you used when solving the problem.

Task 25. The company has 550 employees, 380 of them have higher education, and 412 have specialized secondary education, 357 employees have both higher and specialized secondary education. What is the likelihood that a randomly selected employee has either a secondary specialized, or higher education, or both?

Task 26. 3 cars participate in the rally: the first one can get off the route with a probability of 0.15; the second - with a probability of 0.05; the third - with a probability of 0.1. Determine the probability that they will arrive at the finish:

1. only one car;
2. two cars;
3. at least two cars.

Task 27. The company sells cars. The likelihood that during the warranty period due to the fault of the manufacturer there will be malfunctions in the chassis of the machine - 0.01, in the engine - 0.005, in the control system - 0.003. What is the likelihood that during the warranty period due to the fault of the manufacturer there will be any malfunctions in the named parts of the machine?

Task 28. The owner of the car decided to urgently sell it. On advertising, he wrote out the coordinates of people who want to buy a car of such a make and age as his car, after which he shows the car in turn to each potential buyer. The probability of selling a car to each of them is estimated at 0.05. What is the likelihood that the third potential buyer will buy the car?

Task 29. The company produces memory elements for computers. The buyer checks 5 items from a large batch. If at least one element is defective, the batch will not be accepted. What is the probability of failure if it is known that 1% of the elements contain a defect?

Task 30. The company produces two types of products A and B. The demand for one of these products does not depend on the demand for the other. The probability of a drop in demand for product A in the next quarter is 0.4; the probability of a drop in demand for product B in the next quarter is 0.2. What is the likelihood that demand will fall in the next quarter

a.at least one of these products?

b.for both products?

Task 31. There are 2 sensors in the office that signal a fire. The probability of each of them triggering in the event of a fire in the room is 0.95. Find the likelihood that:

a.both sensors work;

b.not a single sensor will work;

c.exactly one sensor will work?