Events and Their probabilities. Statistics
16. There are 20 students in the group. Of these, 12 work. What is the likelihood that a randomly asked student is working? 17. Interviewed 300 car owners of one model - what was decisive for them when buying a car: price, appearance, body color, interior comfort, engine power? For 90 people, the determining factor was the price, for 30 - the body color, for 60 - the appearance, for 45 - the comfort of the cabin, for 75 - engine power. What is the probability that the owner of a car randomly chosen from these 300 bought it mainly because of the comfort of the cabin? 18. What is the probability of removing the king from the deck of cards (36 cards)? 19. 20 shots were fired for the target, with 18 hits recorded. Find the relative frequency of hitting the target. 20. When testing a batch of devices, the relative frequency of suitable devices turned out to be 0.9. Find the number of suitable devices, if only 200 devices were tested. 21. Determine the probabilities of the following events for the dice experience: a) the loss of the number 4; b) loss of a number greater than 2; c) occurrence of an odd number. 22. What is the probability that with the simultaneous throwing of two dice, the following events will occur: a) loss of points 10; b) loss of points less than 4; c) loss of an odd amount of points. 23. Two dice are thrown simultaneously. Event A - the amount of points dropped is more than ten, event B - this amount is less than four. Which of these events is more likely? 24. In the box there are 15 parts, among which 10 are painted. The random collector retrieves two parts. Find the likelihood that the extracted parts will turn out to be colored. 25. There are 50 parts in the box, of which 5 are defective. Four parts are extracted at random. Find the probability that among the extracted parts: a. no defective; b. no standard 26. Dialing a phone number, the subscriber forgot the last two digits and, remembering only that these numbers are different, dialed them at random. Find the probability that the desired numbers are dialed. 27. Four men and six women work in the workshop. Seven people were randomly selected by personnel numbers. Find the likelihood that three women will be among the selected individuals. 28. The group has 15 students, including 10 excellent students. 7 students were selected on a random list. Find the likelihood that there are five excellent students among the selected students. 29. There are 15 students in the group. Of these, 10 work. What is the likelihood that a randomly asked student is working? 30. Interviewed 340 car owners of one model - what was decisive for them when buying a car: price, appearance, body color, interior comfort, engine power? For 90 people, the determining factor was the price, for 40 - the body color, for 70 - the appearance, for 55 - the comfort of the cabin, for 85 - engine power. What is the probability that the owner of a car randomly chosen from these 340 bought it mainly because of the comfort of the cabin? 31. When testing a batch of devices, the relative frequency of suitable devices turned out to be 0.8. Find the number of suitable devices, if only 300 devices were tested
