Conditional Probability

Whenever we deal with conditional Probability we need to have knowledge about the word probability. Generally people have a rough idea about its meaning. In our day-to-day life we came across statement like, probably it may rain today, he may join politics or American team has a good chance of winning the world cup. When we use terms like: possible, chance, likely etc. all these terms convey the same sense that the event is not certain or in other words there is an uncertainty about the occurrence (or happening) of the event. Conditional Probability consist of two events, these events can be independent or can be dependent. Suppose, if we have two events ‘A’ and ‘B’ then we have the conditional probability Formula:
p(A/B)=p(B ∩ A)/p(A) and   p(B/A)  =p(A ∩ B)/p(A),
p(A/B) is the probability of ‘A’ when ‘B’ has already occurred and p(B/A) is the probability of ‘B’ when ‘A’ has already occurred.
With the help of conditional Probabilities we can find the probability of two Independent Events suppose if we are given a Set of playing cards and we are asked to find the probability of a black card greater than 4 and less than 5 than we can solve this problem with the help of conditional probability, let ‘A’ be the event for getting card greater than 4 and less than 5 and ‘B’ be the event of getting black card. Now we need to find the probability of ‘A’ when ‘B’ has already occurred and for that we have the formula given above with the help of this formula we can easily find the probability.
This is all about conditional probability.