Probability : Probability S.M.Popade
smpopade@yahoo.co.in
+919822772673 Reliance Maths Academy Parbhani
DEFINITIONS : DEFINITIONS Experiment
An experiment is a set of actions (processes terms), which are carried out under stipulated conditions to study the phenomena associated with it. Broadly, there can be two types of experiments:
(i) Experiments with definite outcome:
These type of experiments are certain in nature. Outcomes of experiments are known in advance.
(ii) Experiments with indefinite outcome:
These type of experiment are uncertain in nature, we cannot predict the outcome with certainty. Reliance Maths Academy Parbhani
Random Experiment : Random Experiment An experiment whose all possible outcomes (results) are known in advance, but the result of any specific performance cannot be predicted before completion of the experiment.
Illustrations: Reliance Maths Academy Parbhani
Slide 4 : Reliance Maths Academy Parbhani
Sample Space : Sample Space The set of all possible outcomes of an experiment (or trial) is called the sample space. It is usually denoted by s.
Illustrations:
Slide 6 : Reliance Maths Academy Parbhani
Event : Event The appearance of a particular outcome, which we may find in the sample space, is an event. Any subset of the sample space is called an event.
Illustrations: Reliance Maths Academy Parbhani
Complement of an Event: : Complement of an Event: Let S be the sample space and A be some events, then the set of all out comes which are in S but not in A is called the complete of event A. It is denoted by A| or Ac.
Illustrations: Reliance Maths Academy Parbhani
Mutually Exclusive Events: : Mutually Exclusive Events: Let the two events be A and B. If occurrence of event A excludes the possibility of occurrence of B and vice-versa, then we say that A and B are mutually exclusive event i.e. they cannot occur simultaneously. It (i.e. mutual exclusion) can happen only when the sets of two events have no common point.
Illustrations: Reliance Maths Academy Parbhani
Slide 10 : Reliance Maths Academy Parbhani
Equally likely Events: : Equally likely Events: Two or more events are said to be equally likely when there is no reason to prefer one event over other i.e. they have equal (not same) number of points in their sets.
Illustrations: Reliance Maths Academy Parbhani
Exhaustive Events: : Exhaustive Events: If n events A1, A2, ........., An related to any particular sample space are such that if we take union of the sets of all the n events, sample space is formed. i.e.
A1 ? A2 ? A3 ? ............... ? An = S
Illustrations: Reliance Maths Academy Parbhani
Mutually Exclusive and Exhaustive Events. : Mutually Exclusive and Exhaustive Events. Events A1, A2, .......... An are said to be mutually exclusive and exhaustive if they satisfy the condition for mutual exclusion and exhaustiveness both.
A1 ? A2 ? A3 ? ............... ? An and Ai n Aj = F, where i = 1, 2, ........., n and
j = 1, 2, ........... n and i ? j.
Illustrations: Reliance Maths Academy Parbhani
Introduction To Probability : : Introduction To Probability : If n represents the total number of equally mutually exclusive and exhaustive possible outcomes of an experiment and m of them are favourable to the event A, then the probability of the event A is defined as
P(A) = n(E)/n(S) = m/n
This is known as classical definition of probability Reliance Maths Academy Parbhani
Note : : Note : (i) for any event A, A ? S.
(ii) 0 < P(A) < 1, P(A) ? R
(iii) P(A) + P(A|) = 1
(iv) If ‘a’ cases are favourable to an event A and ‘b’ cases are favourable to an event A| (i.e. unfavourable to A) then P(A) = a/(a+b) and
P(A| ) = b/(b+a).
We say that odds in favour of A are a : b
and odds against of A are b : a Reliance Maths Academy Parbhani