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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 dened 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 dened 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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