Task 1 Combinatorics

In how many ways can you seat 6 guests at a round table?

Task 2 Events and Their Probabilities

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.

Task 3 Basic relationship

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 4 Total probability rule Bayes law

The probability that the bank's client will not repay the loan during the period of economic growth is 0.03, during the period of the economic crisis 0.14. Suppose the probability that a period of economic growth begins is 0.6. What is the probability that a randomly selected bank client will not return the loan?

Task 5 Sequences of Independent Trials (Bernoulli s formula)

Mr. A is a real estate agent. On average, 20% of customers who turn to him make purchases. Over the past week, 8 clients have approached him.

What is the likelihood of at least four customers making purchase

Task 6 Discrete distributions

Suppose that the average number of visitors arriving at the bank within 30 minutes is 5. The bank needs to know the probability that 4 visitors will arrive at the bank within 30 minutes.

Task 7 Continuous Probability Distributions

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions.

1. What is the probability of completing the exam in one hour or less?
2. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes?