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G O Y A L B R O T H E R S P R A K A S H A N

Assignments in Mathematics Class X (Term II)

•

The science which measures the degree of uncertainty is called

probability.

•

There are two types of approaches to the study of probability. These are experimental or empirical approach and theoretical approach.

•

In the experimental approach to probability, we

nd the probability of the occurrence of an event

by actually performing the experiment a number of

times and record the happening of an event.

•

In the theoretical approach to probability, we predict the results without actually performing the experiment.

•

The observations of an experiment are called its

outcomes

.

•

An experiment in which all possible outcomes are known and the exact outcome cannot be predicted

in advance, is called a

random experiment

.

•

The word

unbiased

means each outcome is equally likely to occur. For example, an unbiased die indicates that each of the outcomes 1, 2, 3, 4, 5 or 6 has equal chances to occur. Throughout this chapter, we shall

assume that all the experiments have equally likely

outcomes.

•

The theoretical probability of an event E, written as P(E) is dened as

P(

E)

Number of outcomes f

avourable

to

E

Total number of all possible

=

ooutcomes of the experiment

15. PROBABILITY

IMPORTANT TERMS, DEFINITIONS AND RESULTS

•

An event having only one outcome of the experiment is called an elementary event.

•

The sum of the probabilities of all the elementary

events of an experiment is 1.In general for any event EP(E) = 1 – P(not E) = 1 –

P(E)

or

P(E)

= 1 – P(E)or P(E) +

P(E)

= 1Here the event

E,

representing not E, is called the compliment of the event E.

•

The probability of the event which is impossible to occur is 0. Such an event is called an

impossible event

.

•

The probability of an event which is sure (or certain) to occur is 1. Such an event is called a

sure

or a

certain event

.

•

For an event E, we have 0

<

P(E)

< 1.

•

A die is a well balanced cube with its six faces marked with numbers or dots 1 to 6. When we throw a die we are interested in the number that occurs on the top face.

•

The pack or deck of playing cards consists of 52 cards, 26 of red colour and 26 of black colour. There are four suits each of 13 cards namely hearts (

♥

),

spades (

♠

), diamonds (

♦

) and clubs (

♣

).Each suit contains ace, king, queen, jack or knave,

10, 9, 8, 7, 6, 5, 4, 3, 2.

There are 4 aces, 4 kings, 4 queens, 4 jacks, 4 tens,

and so on in a pack.

Kings, queens, and jacks are called face cards.

SUMMATIVE ASSESSMENT

MULTIPLE CHOICE QUESTIONS

[1 Mark]

A. Important Questions

1.

The theoretical probability P(E) of an event E is dened as : (a)

P(

E)

No.ofallpossibleoutcomesoftheexperiment No.ofoutcomesf

=

a

avourable

to

E(b) P(E) = No. of outcomes favourable to E × No.

of all possible outcomes of the experiment

(c)

P(

E)

No.ofoutcomesf

avourable

to

E

No.ofallpossibleoutcomesoft

=

hheexperiment

(d) none of these

2.

Which of the following can be the probability of

an event?(a) – 0.02 (b) 1.4 (c)

2526

(d)

54

3.

Which of the following cannot be the probability

of an event? (a)

13

(b) 0.2 (c) 4% (d)

1715

4.

Getting a number 8 in a single throw of a die

is :

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