What is meant by conditional probability?explain with examples and in detail?
Conditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability is written P(A|B), and is read “the probability of A, given B”. Consider the probability of having the habit of smoking, say, in the whole population of a country. This is the unconditional probability “to be a smoker”. The probability that a person is a smoker, given that the sex is “female” (or age is “below 14”, or racial group is “white”, etc.) are examples of conditional probability. One more example is: Suppose we want to know the probability that a total of 8 will turn up when we roll two dices. Ordinarily, we know that the probability this will happen is 5/36. However, suppose we roll one of the dice first. Then we will have a better idea about how likely we are to get 8. For instance, suppose we get a 5 on the first die. Then, to get a total of 8, we need to roll a 3 on the second die, and we know that the probability of this happening is 1/6. Therefo
