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Task 1 Combinatories 18. Given the letters in the word LECTURE in how many ways can two ofthe letters be arranged such that one is a vowel and one is a consonant? Task 2 Events and Their Probabilities 18. What is the probability of removing the king from the deck of cards (36 cards)? Task 3 Basic relationship 18. The marketing department ofthe 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? 4 Total prob ability rule Bayes law 18. Suppose that by the level of risk of not repaying the loan, the bank divides the issued loans into 3 categories: A - good, B - medium risk, C bad. [n 90% of cases, a good loan is repaid on time, an average loan is repaid on time in 70% of cases, and bad in 40% of cases. 60% of loans issued by the bank are good, 30% are medium and 10% are bad. a. What is the likelihood that a randomly selected loan from the list will be paid on time? b. What is the share of good loans among repayments on time? Task 5 Sequences of Independent Trials (Bernoulli s formula) 18. The restaurant manager knows from experience that 70% of people who made an order for the evening will come to dinner at the restaurant. One evening, the manager decided to accept 20 orders, although the restaurant had only 15 free tables. What is the likelihood that more than 15 visitors will come to the ordered seats? Task 6 Discrete distributions 18. Assume a Poisson distribution with PL = 5.0. What is the probability that l. a.X=l? 2. b.Xl? 4. d.Xsl? Task 7 Continuous Probability Distributions 18. Given a standardized normal distribution (with a mean ofO and a standard deviation of I}, what is the probability that Zis between 1.57 and 1.84? Zis less than l.57' or greater than 1.84? What is the value onif only 2.5% of all possible Z values are larger? Between what two values on (symmetrically distributed around the mean) will 68.26% of all possible Zvalnes be contained? P-PP'P