Concept of Probability | Communication Systems
A probability refers to the percentage chance that something will or will not happen. Probability of any event is a number between 0 and 1. If we are sure that the event will occur, we say that its probability is 100% or 1. But if we are sure that the event will not occur, we say that its probability is 0. Note that the probability measures the amount of uncertainty. The concept of probability is required for understanding of communication systems and many other real-life subjects.
Probability = 1 ———-> the required event is certain to occur (sure event)
Probability = 0 ———> No chance of occurring (impossible event)
The word ‘Probability’ is used very often in our daily life; such as ‘probably it will rain in the evening’, ‘what is the probability of getting double head in a throw of a pair of coins?’ and so on.
Fundamental rules of counting
Rule 1 (Fundamental rule of counting):
Suppose one operation has m possible outcomes and that a 2nd operation has n outcomes. The number of possible outcomes when performing the first operation followed by 2nd operation = mxn. It can be extended to 3 or more variables
Ex 1: If coin is tossed 5 times, total outcomes = 2x2x2x2x2 = 32 = 25
Ex 2: If die is thrown and a coin is tossed, how many different outcomes are possible?
Die outcomes = 6 = {1,2,3,4,5,6}
Coin outcome = 2 = {H, T}
Total outcomes (rule 1) = 6×2 = 12
Sample space = {(1,H), (2,H), (3,H), (4,H), (5,H), (6,H),), (1,T), (1,T), (1,T), (1,T), (1,T)}
Rule 2 (Fundamental rule of counting):
The number of possible outcomes of 1st operation or 2nd operation = m + n
