Of the 500 students in one dorm, 300 have engaged in binge drinking, 150 have engaged in social misconduct, and 55 have engaged in both binge drinking and social misconduct. For the students in this dorm, are the characteristics of engaging in social misconduct and binge drinking independant or dependant of each other? Justify answer.
Of the 500 students in one dorm, 300 have engaged in binge drinking, 150 have engaged in social misconduct, and 55 have engaged in both binge drinking and social misconduct. For the students in this dorm, are the characteristics of engaging in social misconduct and binge drinking independant or dependant of each other? Justify answer.
Independent Events:
The events A and B are said to be independent, if the result of one of the events does not depend on the results of the other events. In other words, the events A and B are said to be independent, if the occurrence or non-occurrence of A does not affect the occurrence or non-occurrence of B in any way, and vice-versa.
In terms of probability, independence can be easily determined with the help of the intersection probability of the two events.
Suppose P (A) and P (B) are the probabilities of A and B respectively, and P (A ∩ B) is the probability of the intersection of A and B, that is, the probability that both A and B occur simultaneously.
If A and B are independent, P (A ∩ B) = P (A) ∙ P (B).
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