NCERT Book Class 10 Maths Chapter 14 Probability

202 MATHEMATICS

PROBABILITY 14
The theory of probabilities and the theory of errors now constitute
a formidable body of great mathematical interest and of great
practical importance.
– R.S. Woodward

14.1 Probability — A Theoretical Approach
Let us consider the following situation :
Suppose a coin is tossed at random.

When we speak of a coin, we assume it to be ‘fair’, that is, it is symmetrical so
that there is no reason for it to come down more often on one side than the other.
We call this property of the coin as being ‘unbiased’. By the phrase ‘random toss’,
we mean that the coin is allowed to fall freely without any bias or interference.

We know, in advance, that the coin can only land in one of two possible ways —
either head up or tail up (we dismiss the possibility of its ‘landing’ on its edge, which
may be possible, for example, if it falls on sand). We can reasonably assume that each
outcome, head or tail, is as likely to occur as the other. We refer to this by saying that
the outcomes head and tail, are equally likely.
For another example of equally likely outcomes, suppose we throw a die
once. For us, a die will always mean a fair die. What are the possible outcomes?
They are 1, 2, 3, 4, 5, 6. Each number has the same possibility of showing up. So
the equally likely outcomes of throwing a die are 1, 2, 3, 4, 5 and 6.