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
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
An experiment in which all possible outcomes are known and the exact outcome cannot be predicted
in advance, is called a
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
The theoretical probability of an event E, written as P(E) is dened as
Number of outcomes f
Total number of all possible
ooutcomes of the experiment
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 –
= 1 – P(E)or P(E) +
= 1Here the event
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
The probability of an event which is sure (or certain) to occur is 1. Such an event is called a
For an event E, we have 0
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 (
), 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.
MULTIPLE CHOICE QUESTIONS
A. Important Questions
The theoretical probability P(E) of an event E is dened as : (a)
E(b) P(E) = No. of outcomes favourable to E × No.
of all possible outcomes of the experiment
(d) none of these
Which of the following can be the probability of
an event?(a) – 0.02 (b) 1.4 (c)
Which of the following cannot be the probability
of an event? (a)
(b) 0.2 (c) 4% (d)
Getting a number 8 in a single throw of a die