Let an experiment be repeated , under the same conditions as the result of the several possible out comes. The experiment is called as trial and the possible outcomes are called events or cases.
-Tossing of a coin is a trial and turning up of head or tail is an event -Throwing a die is a trial and getting 1 or 2 or 3 or 4 or 5 or 6 is an event
The total no of all possible outcomes in any trial is known as exhaustive events. Ex(1): In tossing a coin, there are two exhausive cases, i.e. head or tail Ex(2): In tossing a dice, there are six exhausitive cases
The cases which entail (considerable risk) the happening of an event are said to be favourable events. EX: When we through the two dices the no. of favourable of getting a sum of 6 is 5: (1,5),(5,1)(2,4)(4,2)(3,3)
No two or more than two of them can happen simultaneously in the same trial. EX(1):In a tossing a coin can either the head will come or tail. If the head will come, the possibility of getting tail in the same trial is ruled out. EX(2):In throwing a dice all 6 faces numbered 1,2,3,4,5,6 are mutually exclusive since any outcome rules out the possibility of getting other.
Occurences which can be repeated a number of times, essentially under the same conditions and whose result cannot be predicted before are known as random experiment. EX: rolling of a dice, tossing a coin, taking out balls from a bag.
The set of all these possible outcomes is called the sample space for the particular experiment and is denoted by an 's'.
If a coin is tossed and Head and Tail denote with H and T respectfully then the sample space is:
S={H,T}
Where there are two sample points H and T. S={1,2,3,4,5,6}. In case of coin there are six sample points.
If the no of sample points in a sample space is finite, we call it a finite sample space.
Note:
S⊆S; where S itself is an event
Φ⊆S; the null set is also an event
'Axioms' are statements which one reasonably true and accepted as such without seeking any proof. Definition: Let S be the sample space associated with a random experiment . Let A be any event in S, then P(A) is the probability of occurence of A if the following axioms are satisfied.
P(A)>0; where A is any event
P(S)=1; P(A)+P(B)+....+P(n)=1
P(AUB)=P(A)+P(B); when event A and B are mutually exclusive.