Finite Probability is a very important concept in discrete mathematics. Before we begin let’s understand some basic terminology, that is important in understanding probability theory.
|THROW A DICE AND YOU GET A NUMBER|
Probability of an event is denoted as P(E) and 0 < = P(E) <= 1.
When an event occur then it is a favorable outcome when it happens.
When the event does not happen then it is an unfavorable outcome as it did not happen. Sometimes, we also need to find unfavorable outcomes of an event.
An event is equally likely if the probability of each outcome in sample space is equally likely.
For example, when we toss a coin we get either Head or Tail out of two outcomes of the sample space. So there is a 50-50 chance of getting a Head or Tail and both are equally likely events.
|HEAD OR TAIL ARE EQUALLY LIKELY EVENTS|
Formal Definition of Probability
If S is a finite non-empty sample space of equally likely outcomes and E is an event, that is, a subset of S, then the probability of E is
P(E) = |E| / |S|
A box contains 3 Red balls and 5 Green balls. What is the probability that a ball picked randomly from the box is Red?
Total Number of Balls in Box = 3 + 5 = 8
Sample Space = 8
There are 3 ways to pick Red balls, Therefore, Event E = 3
P(E) = 3/8
The probability of picking a Red ball from the box is 3/8.