NCERT Book Class 12 Maths Chapter 13 Probability

406 MATHEMATICS

Chapter 13
PROBABILITY

v The theory of probabilities is simply the Science of logic
quantitatively treated. – C.S. PEIRCE v

13.1 Introduction
In earlier Classes, we have studied the probability as a
measure of uncertainty of events in a random experiment.
We discussed the axiomatic approach formulated by
Russian Mathematician, A.N. Kolmogorov (1903-1987)
and treated probability as a function of outcomes of the
experiment. We have also established equivalence between
the axiomatic theory and the classical theory of probability
in case of equally likely outcomes. On the basis of this
relationship, we obtained probabilities of events associated
with discrete sample spaces. We have also studied the
addition rule of probability. In this chapter, we shall discuss
the important concept of conditional probability of an event
given that another event has occurred, which will be helpful
in understanding the Bayes' theorem, multiplication rule of Pierre de Fermat
probability and independence of events. We shall also learn (1601-1665)
an important concept of random variable and its probability
distribution and also the mean and variance of a probability distribution. In the last
section of the chapter, we shall study an important discrete probability distribution
called Binomial distribution. Throughout this chapter, we shall take up the experiments
having equally likely outcomes, unless stated otherwise.
13.2 Conditional Probability
Uptill now in probability, we have discussed the methods of finding the probability of
events. If we have two events from the same sample space, does the information
about the occurrence of one of the events affect the probability of the other event? Let
us try to answer this question by taking up a random experiment in which the outcomes
are equally likely to occur.
Consider the experiment of tossing three fair coins. The sample space of the
experiment is
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}