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# Probcha2

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### Probcha2

1. 1. Probability Module 6
2. 2. Probability An Overview
3. 3. Random experiment <ul><li>Experiment with more than One possible Outcome </li></ul><ul><li>‘Experiment Is repeatable </li></ul><ul><li>Outcome is unpredictable </li></ul><ul><li>outcomes of which vary from repetition and Repetition </li></ul>
4. 4. Basic Concepts of probability <ul><li>Probability is the chance of something to happen </li></ul><ul><li>Eg. If we are tossing a coin we can enumerate the possible outcomes. The outcomes are either head or tail, There is an uncertainty. They may or may not be happen. The value of Probability lies between 0 and 1 </li></ul><ul><li>The probability ‘0’ means something can never happen. Probability ‘1’ mean s something can happen </li></ul>
5. 5. Types of Probabilities <ul><li>There are 4 types of Probabilities </li></ul><ul><ul><li>Classical or priori or mathematical </li></ul></ul><ul><ul><li>Statistical or empirical or a posterior of Probability or Relative Frequency </li></ul></ul><ul><ul><li>Axiomatic approach </li></ul></ul><ul><ul><li>Subjective or PersonalisticApproach </li></ul></ul>
6. 6. Classical definition <ul><li>Consider the random experiment has ‘N’ possible outcomes of which ‘m’ favourable to the event A Then </li></ul><ul><ul><ul><ul><ul><li>Favourable number cases </li></ul></ul></ul></ul></ul><ul><li>probability of A = </li></ul><ul><li>Total No of cases </li></ul><ul><li>m </li></ul><ul><li>P(A) = ----- </li></ul><ul><li>N </li></ul>
7. 7. Axiomatic Probability <ul><li>Let ‘s’ the sample space and A be event and ‘A’ be number of probabilities </li></ul><ul><li>P(A) satisfies the following axioms </li></ul><ul><li>P(A) lies between 0 and 1 </li></ul><ul><li>P(s)=1 </li></ul><ul><ul><li>= P(A) + P(B) if A and B are Mutually exclusive </li></ul></ul>
8. 8. Relative Frequency theory <ul><li>Consider a random experiment . Let ‘A’ be an event; Let the experiment is repeated ‘N’ times . Let the event happen in ‘m’ out of these N Repetitions and fail to happen ‘N-m’ repetitions .Then the ratio m/N is called relative frequency. </li></ul><ul><li>P(A)=Lim M/N </li></ul><ul><li>N->  </li></ul><ul><li>When the number of repetitions are made larger and larger the probability of happening of the event is being assumed that that the limit is finite and unique. Ie m/N approaches to a particular value. </li></ul><ul><li>When N tends to infinity P(A) =m/N </li></ul>
9. 9. Personalitic View of Probability <ul><li>As a measure of personnel confidence in a particular position </li></ul><ul><li>-depends on Degree of belief </li></ul>
10. 10. Sample point <ul><li>The simple outcome of a random experiment is called a Sample Point </li></ul><ul><li>Eg. Tossing a coin getting a head is a sample point </li></ul><ul><li>Tossing a die getting odd numbers </li></ul>
11. 11. Sample space <ul><li>The set of all possible outcomes of a a random experiment is called a sample space </li></ul><ul><li>Tossing a coin ,getting a head and tail are the sample space {H,T} </li></ul>
12. 12. Event <ul><li>A subset of the sample space is called an event </li></ul>
13. 13. Relations of operations of Events <ul><li>Equality of Events </li></ul><ul><ul><ul><li>It is denoted by A=B </li></ul></ul></ul><ul><ul><ul><li>A={1,2,3,4,5} </li></ul></ul></ul><ul><ul><ul><li>B={1,2,3,4,5} </li></ul></ul></ul>
14. 14. Compliment of an event <ul><li>The elements of the sample space and not in the elements of the given element A then A c </li></ul><ul><li>A 1 or A </li></ul><ul><li>S = {1,2,3,4,5,6} </li></ul><ul><li>A = {1,3,5} </li></ul><ul><li>A c = {2,4,6} </li></ul>
15. 15. Union Of Events <ul><li>The union of two events A and B is the element in A or in B That is union means at least one among the given events </li></ul><ul><li>S = {1,2,3,4,5,6} </li></ul><ul><li>A = {1,3,5} </li></ul><ul><li>B = {2,4,5,6} </li></ul><ul><li>A  B= {1,2,3,4,5,6} </li></ul>
16. 16. Intersection Of events <ul><li>Intersection of two events A and B is the element in both A & B .It is denoted as A  B </li></ul><ul><li>S = {1,2,3,4,5,6} </li></ul><ul><li>A = {1,3,5} </li></ul><ul><li>B = {2,4,5,6} </li></ul><ul><li>A  B= {5} </li></ul>
17. 17. Mutually exclusive events <ul><li>Two events are said to be mutually exclusive events if the occurrence of one event prevents the occurrence of the other event </li></ul><ul><li>Tossing a coin- The occurrence of Head prevents the occurrence of tail </li></ul><ul><li>If A and B are mutually exclusive Then A  B = { } </li></ul>