What is Probability

Probability - The chance that something will happen

It is the chance of an event occurring or an event that may be chosen, happened or done out of several possible alternatives occurrence.

Probability = the number of outcomes of favourable event / the total number of possible

Experiment: activity with some possible outcomes.

Ex: Throwing a dice

Outcome: Output or result of an experiment.

Ex: any number may come {1, 2, 3, 4, 5, 6}, hence number of possible outcome is 6

Sample space is the set of all possible outcomes of the experiment,

Ex: Sample space is (S) = {1, 2, 3, 4, 5, 6}

Events are the subsets of the sample space.

Ex: chance of getting any one number from {1, 2, 3, 4, 5, 6}

Atomic Event: cannot be further decomposed, and mutually exclusive - either this                                   occurs or another but never both 
Ex: either Charlie is at work Charlie is at home, but cannot be at the same place at same time

Composite Events: could be further decomposed

Ex: In a dice throw is at least ‘5’ or most ‘5’ or even number (i.e. in {2, 4, 6})

 Completeness of Probability: coverage of all possible outcomes

 

Conditional Probability:  Conditional probability is finding the probability of an event based on a    given   condition or information.

  Without condition the sample space is whole union - (AᴗB), but in conditional probability the sample     space shrinks in two parts - P(B) and (AᴖB).

Example:  

 

 P(A|B)    =     P(AᴖB) / P(B)

P(A)= Probability in question

P(B)= Probability of B  (probability of B is Given as a condition)

AᴖB = A intersection B ( A & B)

AᴗB = A Union B (all together)

Let’s assume there are 100 students in a class, 40 likes Apple, 30 likes Banana and 20 likes both Apple & Banana.

Given That

A=40

B=30

AᴖB =20

Formula for Conditional probability is P(A|B)    =  P(AᴖB) / P(B)    
P(B)  = 30/100  = 0.3

P(AᴖB) = 20/100 = 0.2

So P(A|B)   = 0.2 / 0.3 = 0.67

What is Bayes Rule? | What is Bayes Theorem?| What is Bayes Law?