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Dependent and Independent Events:

An Independent Event is an event whose whose outcomes are not affected by another event. Two independent events A and B satisfy:


A Dependent Event is an event that is affected by pervious events. In order to understand dependent events, we have to introduce conditional probability. Conditional probability is the probability of an event A given that another event B has already occurred. The following notation is used to denote a conditional probability


Two dependent events A and B satisfy:


Example: In an experiment we roll two dice. Event A is the sum of the two dice is 10 and event B is the number on each die is the same. Are A and B independent?
The sample space for this experiment consists of 36 pairs. We write down the elements of A and B:


The intersection of A and B is:


We find the following probabilities:

Now, we check to see whether A and B satisfy the formula for independent events:

Since A and B do not satisfy the formula for independent events, they have to be dependent.


Example: Find  for the previous example.
We use the formula :