PRACTICAL CLASS № 13-14

Basic concepts of probability theory. The classification of events. The classical definition of the event probability. Addition and multiplication theorems of probabilities. The formula of total probability. The formula of Bernoulli, Poisson's ratio

Theoretical questions:

1. Main concept. Definition of probability

2. Properties of probability

Classroom assignments:

1.In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?

2. If we throw a fair die, any one of the six numbers 1, 2, 3, 4, 5 and 6 may come up. There are altogether 6 possible outcomes and the occurrence of each of these outcomes is equally likely. Hence, we conclude that each number has an equal chance to appear and the probability of throwing, say, the number ‘1’ is equal to .

The probability for the event: ‘number 5 comes up’ is denoted by . In fact, .

Think!

In a single throw of a die, what is the probability of getting

(a) an odd number?

(b) an even number?

(c) a prime number?

(d) a number greater than 4?

(e) a number from 1 to 6?

(f) a number except 5?

3. Three people are to be seated on a bench. How many different sitting arrangements

are possible if Erik must sit next to Joe?

4. How many 3-digit numbers satisfy the following conditions: The first digit is

different from zero and the other digits are all different from each other?

5. Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara

have, if she doesn’t wear 2 specific shirts with 3 specific pants?

6. A credit card number has 5 digits (between 1 to 9). The first two digits are 12 in

that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit

is 3 times the sixth (which is any number bet 1-9). How many different credit card

numbers exist?

7. In jar A there are 3 white balls and 2 green ones, in jar B there is one white ball

and three green ones. A jar is randomly picked, what is the probability of picking up a

white ball out of jar A?

Homework:

Theoretical material: Random variables, their types. Numerical characteristics of continuous random variables.

Solve problems:

1. If a card is drawn from a pack of 52 playing cards, any one of 52 cards may come up. There are altogether 52 possible outcomes and the occurrence of each of these outcomes is equally likely.

Think!

If we draw a card from a pack of 52 playing cards, what is the probability of getting

(a) the ace of diamonds?

(b) a card of heart?

(c) a card of number 8?

2. When a baby is born, the probability that it is a boy or a girl is theorectially equal,

i.e. .

Think!

If a woman has three daughters, what is the probability that the next baby is a boy?

3. When a card is drawn from a pack of 52 playing card, what is the probability of getting

(a) an ace and a heart?

(b) an ace or a heart?

4. Out of a box that contains 4 black and 6 white mice, three are randomly chosen.

What is the probability that all three will be black?

5. There are 18 balls in a jar. You take out 3 blue balls without putting them back

inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls

were there in the beginning?

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