INTRODUCTION:
Probability is the study of mathematics which calculates the degree of uncertainty. There are two types of approaches to study probability-
Experimental or Empirical Probability
The result of probability based on the actual experiment is called experimental probability. In this case, the results could be different if we do the same experiment again.
P (E) = (Number of the trials in which the event happened. )/(Total number of the trials )
Probability:
In the theoretical approach, we predict the results without performing the experiment actually. The other name of theoretical probability is classical probability.
P (E) = (Number of outcomes favourable to E )/(Total number of all possible outcomes)
where the outcomes are equally likely.
Equally Likely Outcomes:
If we have the same possibility of getting each outcome then it is called equally likely outcomes.
Example:
A dice have the same possibility of getting 1, 2, 3, 4, 5 and 6.
Not Equally Likely:
If we don’t have the same possibility of getting each outcome then it is said to be the not equally likely outcome.
Example:
3 green balls and 2 pink balls are not equally likely as the possibility of the green ball is 3 and the possibility of the pink ball is 2.
Elementary Event:
If an event has only one possible outcome then it is called an elementary event.
Remark:
The sum of the probabilities of all the elementary events of an experiment is 1.
The General form:
P (Heads) + P (Tails) = 1
P (H) + P = 1 where is ‘not H’.
P (H) – 1 = P
P (H) and P are the complementary events.
Impossible Events:
If there is no possibility of an event to occur then its probability is zero. This is known as an impossible event.
Example:
It is not possible to draw a green ball from a group of blue balls.
Sure or Certain Event:
If the possibility of an event to occur is sure then it is said to be the sure probability. Here the probability is one.
This shows that the probability of an event could be
0 ≤ P (E) ≤ 1
The theoretical (classical) probability of an event E, written as P(E), is defined as
P (E) = (Number of outcomes favourable to E )/(Total number of all possible outcomes )
where we assume that the outcomes of the experiment are equally likely.
An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1.
For any event E, P (E) + P ( E ) = 1, where E stands for ‘not E’. E and E are called complementary events.