Unit 4 Theme: Probability of occurence. Grammar: Gerundial Constructions

Objectives: By the end of this unit, students should be able to use active vocabulary of this theme in different forms of speech exercises.

Students should know the Gerundial Constructions till the end of this course.

Methodical instructions: This theme must be worked out during two lessons a week according to timetable.

Lexical material: Introduce and fix new vocabulary on theme “Probability of occurence”.

How long is the branch of science alive?. Discuss in groups.

Grammar: Introduce and practice the Gerundial Constructions. Revise the use of Gerundial Constructions

Probability of occurence

In mathematical language the choice, the probability of success is the ratio of the number of ways in which the trial can succeed to the total number of ways in which the trial can result. Here nothing favors the choice of any particular circle; they are all on the same page, and you are just as likely to cover one as another. The trial can result in five ways; there are five black circles. The trial can result in nine ways; there are nine circles in all (in exercise 1.1). If p represents the probability of success, then p =,5-9..

Similarly, the probability of failure is the ratio of the number of ways in which the trial can fail to the total number of ways in which it can result. If q represents the probability of failure, in this case q =,4-9.. Notice that the sum of probability of success and failure is 1. If you put your finger on a circle, it is certain to be either a black circle or a white one, for no other kind of circle is present. Thus p+q =,5-9.+,4-9.=1. The probability that an event will occur can not be more than 1. When p=1, success is a certainty. When q =1, failure is sure. Let S represent the number of ways in which a trial can succeed. And let f represent the number of ways in which a trial can fail.

𝑝=,𝑆-𝑆+𝑓.;𝑞=,𝑓-𝑆+𝑓.;𝑝+𝑞=,𝑆-𝑆+𝑓.+,𝑓-𝑆+𝑓.=1

When S is greater than f, the odds are S to f in favor of success, thus the odds in favor of covering a black circle are 5 to 4. Similarly, when f is greater than S, the odds are f to S against success. And when S and f are equal, the chances are even; success and failure are equally likely. Tossing a coin illustrates a case in which S and f are equal. There are two sides to a coin, and there is no reason why a normal coin should fall one side up rather than the other. So if you toss a coin and call heads, the probability that it will fall heads is ,1-2.. Suppose you toss a coin a hundred times, for each of the hundred trials, the probability that the coin will come down heads is ,1-2.. You might expect fifty of the tosses to be heads. Of course, you may not get fifty heads.But the more times you toss a coin, the closer you come to the realization of what youexpect.

If p is the probability of success on one trial, and K is the number of trials, then the expected number is Kp. Mathematical expectation in this case is defined as Kp.

Ex.1. Answer the following questions.

a. What does the article deal with?

b. If you were shown 9 red circles and 6 black circles and were asked to choose one

of them which on these circles would you be likely to choose? Why?

c. Can you give the definition of the probability of failure? What is it?

d. What are the odds in casef>S ?

e. What are the odds in casef<S ?

f. SupposeS= f , what would the chances be?

g. Could you give some examples to illustrate a case when S and f are equal?

Ex.2. Are these statements true or false? Correct the false statements.

a. The trial can succeed in nine ways when you suppose that you have nine circles.

b. The sum of the probability of success and failure is equal to 1.

c. The probability that an event will occur can be more than 1.

d. In tossing two coins the fact that one fell heads would not affect the way the other

fell.

Ex.3. Fill in each gap using a word from the text.

a. There are differences of opinion among mathematicians and philoso– phers about ______ theory.

b. Suppose two dice are thrown. What are the chances that the ______of the faces is five?

c. Two coins are ______ simultaneous. Since a coin will come down ______ ( ) or tail (T), each possible outcome is a member of A × A where A = { … , T}.

d. To describe this sample space ______ each situation in terms of events and discuss the chances of each event ______ .

e. When we try to do something several times we say that we have had several ______ .

Ex.4.Listening

Follow the link: http://www.youtube.com/watch?v=LSxqpaCCPvY (Mathematics Gives You Wings)

Grammar: Gerundial Constructions

Do exercises from Unit 59 p.118-119 ex.:59.1-59.4 and Unit 60 p.120-211 ex.:60.1-60.4 (Raymond Murphy “English Grammar in Use” A self-study reference and practice book for intermediate students of English Third Edition. Cambridge)

БӨЖ тапсырмалар:

Retell the text “Probability of occurence.”. Find out new words and translate them. Give a short summary of the text.

Follow the link and pass the test for grammar:

http://www.study.ru/test/test.php?id=385