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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 :