## Probability: Independent and Dependent

In my Probability article, I demonstrated determining the likelihood of events related to students and their grades using a single event.

In this article, I will demonstrate the nature of events used in probability determination – either they are independent or dependent events.

### Independent Events

Returning to the example from the probability article, we determined the probability the student Chris Winns will receive an ‘A’ grade.

If this scenario was determining the likelihood of two students obtaining an ‘A’ grade, that would be an example of an independent event, because the first event (student obtaining an A’ grade) does not affect the probability of the second event.

### Dependent Events

Since the teacher assigning grades is not using a limited number of grades – assigning an ‘A’ grade does not deplete the supply of available ‘A’ grades and she is free to assign as many as she like in the future, that scenario’s events are independent since the first student receiving an ‘A’ grade does not affect the likelihood of a second student receiving the same grade.

Conversely, if the teacher’s supply of ‘A’ grades is limited and assigning one ‘A’ grade means there are less ‘A’ grades to use in the future, then the second event is dependent on the first event.

When using the formula to determine probability for dependent events, you must update the denominator (possibilities) as they decrease with each event.