#theoretical probability

Probability: Likelihood that an event will occur

Two ways to determine probability:

Theoretical- estimated based on chances an event will occur (ie. calculate chances four coins will land heads up)

Previously we have discussed about who invented calculus and In today's session we are going to discuss about Theoretical and empirical probabilities, When we talk about the empirical probability then it is slightly different from the probability we often talk about. Empirical probability is defined for the event e as the fraction of time it takes to produce or occur. Empirical probability is sometimes related with the estimated probability that is nothing but it is an estimation of the Empirical probability. It is defined as if there are a definite number of trials then it will be more accurate then the approximate value.

We describe the empirical probability by the analytical approach as user knows only the behavior of the experiment not the actual experiment so the better way is obtained by the actual experiment that is estimate of the empirical probability. So that is why it is known as estimated probability .

Theoretical probability is defined as the chances of occurrence of an event. If there are an event e then the probability of occurrence of that event is defined as

T . P (theoretical probability) = favorable outcomes of event e / total number of outcomes

In the empirical probability the total outcomes is not define the sample space but it is basically the total number of trials that occurs in the actual experiment .Empirical probability is nothing but the probability that is coming from the observations and sometimes called as probability comes with experience.

There are some examples for defining the theoretical or empirical probability as :

Example : If there is a coin then what is the probability of occurrence of head at the time of tossing it ?

Answer : If the probability of occurrence of tail is known then we estimate the probability of occurrence of head as p (tail) = 1 / 2 then p (head) = 1 – 1/ 2 = 1 / 2.

In the next session we are going to discuss about Theoretical and empirical probabilities and You can visit our website for getting information about geometry help and syllabus for class 12th icse.

Hello students, Previously we have discussed about rules of differentiation and in this section we are going to discuss the Theoretical probability and empirical probability. But first we will see the what is probability, probability means uncertainty. When we are not sure that what is happening and when, then probability comes. Like "he is probably right".

Theoretical probability : - If there are n elementary events ( An outcome of a random experiment is called an elementary event ) associated with a random experiment and m of them are favorable to an event A, then the probability of happening or occurrence of event A is denote by P.

( A ) and is defined as the ratio m / n

Thus, P ( A ) = m / n

Clearly, 0≤m≤n

0≤m / n≤1

=> 0≤P ( A )≤1

If P ( A ) = 1 then A is called a certain event and A is called an impossible event , if P ( A ) = 0, if m elementary events are favorable to an event A out of n elementary events, then the number of elementary events which ensure the non occurrence of that is the occurrence ofĀis n – m.

P (Ā) = n – m / n

=> P (Ā) = 1 – ( m / n )

=> P (Ā) = 1 – P ( A )

=> P (Ā) + P ( A) = 1

Empirical probability :- Suppose we perform an experiment and let n be the total number of trails. The empirical probability of happening of an event E is defined as P ( E ) = number of trials in which the event happened / total number of trials.