Task 13. For the manufacture of parts requires three basic operations. The probability of a defect in the first operation is 0.01, in the second - 0.02, in the third - 0.025. Find the probability of manufacturing a standard part, provided that the appearance of marriage in certain operations is independent.

Task 14. The workshop produces on average 2% of defective parts. Out of every hundred standard parts, on average 70 are first-class. Find the probability that the part manufactured in the workshop will be of the first grade.

Task 15. When transmitting text, 10% of the letters are distorted and received incorrectly. What is the likelihood that all five letters of a given word will be accepted correctly?

Task 16. The probability that a buyer who intends to purchase a computer and software will acquire only a computer is 0.15. The probability that the buyer will buy only the software is 0.1. The probability that both a computer and a software package will be purchased is 0.05. What is the probability that either a computer, or a software package, or a computer and software package together will be bought?

Task 17. The probability that a graduate of the Faculty of Finance will defend the diploma "excellent" is 0.6. The probability that he will defend his diploma "perfectly" and receive an invitation to work at the bank is 0.4. Suppose a student defends a diploma. Find the probability that he will receive an invitation to work in a bank?

Task 18. The marketing department of the company conducts a survey to find out the opinions of consumers on a certain type of product. It is known that in the area where research is conducted, 10% of the population are consumers of the product of interest to the company and can give it a qualified assessment. The company randomly selects 10 people from the entire population. What is the likelihood that at least one of them can expertly evaluate the product?

Task 19. The probability that tomorrow the price of consumer goods will rise is 0.3; the probability that the price of silver rises tomorrow is 0.2, and the probability of a simultaneous increase in prices for consumer goods and silver is 0.06. Are consumer goods and silver prices independent of each other? Explain the answer.

Task 20. One of the most difficult problems of market research is the refusal of consumers to answer questions about consumer preferences, or, if the survey is conducted at the place of residence, the absence of their home at the time of the survey. Suppose a market researcher with a probability of 0.94 believes that the respondent agrees to answer the questionnaire if he is at home. He also believes that the likelihood that the same person will be at home is 0.65. Having such data, estimate the percentage of completed questionnaires.