Higher mathematics test VK 4

Collection of assignments for the discipline "MATHEMATICS" (part 4)
Task 1
Question 1. What event, according to the terminology of the theory of probability, is hitting a target when shooting at a shooting range?
1. A credible event.
2. A possible event.
3. An event compatible with event A if event A consists of missing a target.
4. An event opposite to event A, if event A consists of hitting the target.
5. Not an accidental event.
Question 2. Suppose that event A during k tests took place s times. What is the absolute frequency of occurrence of event A?
one. .
one. .
one. .
4.s.
one. .
Question 3. With six throws of a dice (a dice with numbers from 1 to 6 on the edges), the number 5 fell out 2 times, the number 4 fell out 2 times, and the numbers 3 and 2 fell out 1 time each. What, according to the results of this observation, is the frequency (relative frequency) of the event consisting in the occurrence of the number 3 or the number 4?
one. .
one. .
one. .
one. .
one. .
Question 4. What is the statistical definition of probability?
1. The probability of event A is the ratio of the number of outcomes favorable to event A to the total number of trials in a series of observations.
2. Probability is called a stable frequency of occurrence of an event.
3. Probability is called a constant value around which the observed frequency values ​​are grouped.
4. Probability is the arithmetic mean of the frequency of occurrence of an event during a series of identical tests.
5. Probability is the ratio of the number of favorable outcomes to the number of all equally possible outcomes.
Question 5. Which event is credible?
1. An event favored by more than half of the only possible trial outcomes.
2. Falling out of a positive number when throwing a die.
3. Removing blindly a white ball from an urn containing identical, except for color, white and black balls.
4. Drop the sandwich with butter up.
5. Falling out of different numbers with two throws of the dice.
Task 2
Question 1. When is the event system called complete?
1. If the sum of the probabilities of these events is equal to one.
2. If the events are incompatible and equally possible.
3. If the product of the probabilities of these events is equal to one.
4. If the events are incompatible and the only possible.
5. If the sum of the probabilities of these events exceeds one, and the events themselves are compatible.
Question 2. Suppose that under some test events A and B are possible, the probability of event A, the probability of an event B incompatible with A. Which of the following statements is not always true?
1. Event A is the opposite of event B.
2. Event B is the opposite of event A.
3. If events A and B are the only possible ones, then the system of events A, B is complete.
4. Events A and B are equally possible.
5. An event favored by A and B is credible.
Question 3. What is the probability that when the dice are thrown three times, the number 3 appears three times?
one. .
one. .
one. .
one. .
one. .
Question 4. From an urn, in which 4 white balls and 3 black ones, two balls are drawn at random. (The ball is not returned to the urn after being attracted). The balls in the urn differ only in color. What is the probability that the black ball will be drawn first, and the white ball second?
one. .
one. .
one. .
one. .
one. .
Question 5. When a bullet hits the target, it overturns. Suppose that arrow A is known to hit the target with probability, arrow B is known to hit the target with probability, and arrow C is known to hit the target with probability. Arrows A, B, C simultaneously shot at the target. What is the likelihood that the target will tip over?
one. .
one. .
one. .
one. .
one. .
Task 3
Question 1. What does Bernoulli's formula express?
1. The theorem of addition of probabilities.
2. The probability of an event occurring r times in k independent tests.
3. The probability of occurrence of event A in two independent tests.
4. The probability of occurrence of two joint events in one test.