Do you know how probability and statistics help in analysising data
Friends, today we are going to learn about conditional probability and Statistics and their utility in analyzing the data. First question arise is that, what is a probability? It is a way of telling or expressing a knowledge that an event will occur or has occurred. As we all know that probability of an event occurring given that another event has already occurred is called a conditional probability.
This information can be written mathematically like The mathematical expression which shows the above that an event A occurs , given that an event B is already occurred is:
P(B|A) = P(A and B) / P(A)
Baye’s Formula is the another method which helps to calculate a conditional probability. It states that the probability of event B is the sum of the conditional probabilities of event B given that event A has or has not occurred.
Mathematical expression for the following is:
P(B) = P(B|A)P(A) + P(B|Ac)P(Ac)
And for the two independent events (for event A and event B) the expression is:
P(B)P(A) + P(B)P(Ac) = P(B)(P(A) + P(Ac)) = P(B)(1) = P(B)
Let’s have a Probability problems to understand it better: calculating a probability of getting an even number on the die.
Solution: die has 6 faces so it is written as (1,2,3,4,5,6) and the number of even number faces are (2,4,6). so we can calculate it in such way:
S = 1, 2, 3, 4, 5, 6 and A = 2, 4, 6
as P(A) = number of probability of occurance of event A/ total number of events
P(A) = 3/6 = .5 or ½
Statistics, on the other hand is the practice or science of collecting and analyzing numerical data in large quantities. It is basically a study of the collection, organization, analysis and interpretation of the data. So, the two things probability and statistics together plays an important role in finding out measures of central value, measures of spread of different data and this helps in comparing of two data.
Conditional Probabilities and Statistics plays an important role in analyzing the data. For example if we have to calculate the central value for 4 and 6: It is calculated as (4+ 6)/2 = 10/2 = 5. In various Statistical analysis and experiments performed, the results of these experiments depends on probability distributions. Like if we want to calculate a range then conditional probability helps statistics in finding the answer.
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