Glossary

probability theory – теория вероятностей

reliable event – достоверное событие

random event – случайное событие

vessel – сосуд; trial (experiment) – испытание (опыт, эксперимент)

urn – урна; heads or tails? – орел или решка?

at random – наудачу; to land a prize – получить приз

complete group of events – полная группа событий

equally possible events – равновозможные события

uniquely possible events – единственно возможные события

ace – очко (при игре в кости); die – кость (игральная)

dice – игра в кости, кости; hit – попадание; miss – промах

to shuffle – перемешивать; relative frequency – относительная частота

favorable case – благоприятствующий (благоприятный) случай

mass homogeneous events – массовые однородные события

Exercises for Seminar 1

1.1. There are 50 identical details (and 5 of them are painted) in a box. Find the probability that the first randomly taken detail will be painted.

1.2. A die is tossed. Find the probability that an even number of aces will appear.

1.3. Participants of a toss-up pull a ticket with numbers from 1 up to 100 from a box. Find the probability that the number of the first randomly taken ticket does not contain the digit 5 (toss-up – жеребьевка; to pull – тянуть; ticket – жетон).

1.4. In a batch of 100 details the quality department has found out 5 non-standard details. What is the relative frequency of appearance of non-standard details equal to? (batch – партия)

1.5. At shooting by a rifle the relative frequency of hit in a target has appeared equal to 0,85. Find the number of hits if 120 shots were made (a rifle – винтовка).

1.6. One die is randomly taken from a carefully hashed full set of 28 dice of domino. Find the probability that the second randomly taken die can be put to the first if the first die:

a) is a double;

b) is not double (to hash – перемешивать; double – дубль).

The answer: a) 2/9; b) 4/9.

1.7. A point B(x) is randomly put in a segment OA of the length L of the numeric axis Ox. Find the probability that the smaller of the segments OB and BA has the length which is less than L/4. It is supposed that the probability of hit of a point in the segment is proportional to its length and does not depend on its location on the numeric axis.

1.8. Two persons have agreed to meet in a certain place between 18 and 19 o'clock and have agreed that a person come the first waits for another person within 15 minutes then leaves. Find the probability of their meeting if arrival of everyone within the specified hour can take place at any time and the moments of arrival are independent.

The answer: 7/16.

1.9. Two dice are tossed. Find the probability that:

a) the same number of aces will appear on both dice;

b) two aces will appear at least on one die;

c) the sum of aces will not exceed 6.

1.10. A point is randomly taken inside a circle of radius 5. Find the probability that the point will be inside a proper (equilateral) triangle entered in the circle (a proper triangle – правильный треугольник; equilateral – равносторонний).

The answer: .