1.Are the following events equally possible:

a.Experience - tossing a symmetrical coin; events: A1 = {appearance of the coat of arms}; A2 = {number appearance}.

b.Experience - throwing the wrong (bent) coin; events: A1 = {appearance of the coat of arms}; A2 = {number appearance}.

c.Experience - a shot at a target; events: C1 = {hit}; C2 = {miss}.

d.Experience - tossing two coins; events: D1 = {appearance of two emblems}; D2 = {two digits appear}; D3 = {appearance of one coat of arms and one digit}.

e.Experience - removing one card from the deck; events: E1 = {appearance of a card of pure color}; E2 = {appearance of a card of clubs suit}; E3 = {appearance of the card of the diamonds suit}.

f.Experience - dice roll; events: F1 = {appearance of at least three points}; F2 = {appearance of no more than four points}.

g.Experience - sports lottery draw (6 of 36); events: G1 = {occurrence of a combination of 1 2 3 4 5 6}; G2 = {appearance of a combination of 3 12 6 8 36 16}.

2.List all possible outcomes and indicate whether they are equally possible for the following experiments:

a.tossing two coins;

b.consideration of the last two digits of a telephone number taken at random from a directory;

c.consideration of the sum of the last two digits of the telephone number taken from the directory at random.

3.Indicate whether the following events are elementary:

a)loss of the sum of points 7 when throwing two dice;

b)the loss of two digits in the experiment with three coins;

c)pulling out an ace when randomly choosing a card from the deck;

d)loss of the sum of points 2 when throwing a pair of dice;

e)the loss of three emblems when throwing three coins;

4.What is the likelihood that when you roll a dice, a multiple of three will fall out?

5.Determine the probabilities of the following events for the dice experience:

a) the loss of the number 5;

b) loss of a number greater than 3;

c) occurrence of an even number.

6.What is the probability that with the simultaneous throwing of two dice, the following events will occur:

a) loss of points 11;

b) loss of points less than 5;

c) loss of an even amount of points.

7.Two dice are thrown simultaneously. Event A - the amount of points dropped is more than nine, event B - this amount is less than five. Which of these events is more likely?

8.What is the likelihood that with the simultaneous throwing of two dice, the total amount of points dropped will be nine, and the difference three.

9.A two-digit number has been conceived. Determine the probability that the intended number will be:

a.a randomly named two-digit number;

b.a randomly named two-digit number whose digits are different.

10.In the box there are 15 parts, among which 10 are painted. The random collector retrieves three parts. Find the likelihood that the extracted parts will turn out to be colored.

11.There are 100 parts in the box, of which 10 are defective. Four parts are extracted at random. Find the probability that among the extracted parts:

a.no defective;

b.no standard.

12.Dialing a phone number, the subscriber forgot the last three digits and, remembering only that these numbers are different, dialed them at random. Find the probability that the desired numbers are dialed.

13.Six men and four 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.

14.The group has 12 students, including 8 excellent students. 9 students were selected on a random list. Find the likelihood that there are five excellent students among the selected students.

15.In the "secret" lock on the common axis are four disks, each of which is divided into five sectors, on which the numbers are written. The lock opens only if the disks are mounted so that the numbers on them make up a certain four-digit number. Find the likelihood that when installing disks randomly, the lock will open.

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.