Statistical Independence

Let A and B be two events. These events are said to be statistically independent if and only if

The logical basis for the definition of statistical independence is best seen in terms conditional probabilities and is most appealing from a subjective view of probability. Suppose that I believe the probability that event A will occur is P(A). Then I am given the information that event B has occurred. If this new information does not change my view of the probability of A,
 then P(A) = P(A/B), and the information about the occurrence of B is of no value in determining P(A). This definition of statistical independence agrees with a commonsense notion of “independence”.

Example: Probability of College Degrees (Statistical Independence)
Suppose that women obtain 48% of all bachelor degrees in a particular country and that 17.5% of all bachelor degrees are in business. Also, 6% of all bachelor degrees go to women majoring in business. Are the events “Bachelor degree holder is a women” and “Bachelor degree is in business” statistically independent? 

Solution: Let A denote the vent “Bachelor degree holder is a women” and B the event “Bachelor degree is in business” and we have

Thus, in the country of interest only 34.3% of business degrees go to women, whereas women const itute 48% of all degree recipients.