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Similarities between independent and dependent events

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2 Answers

Suppose you had a bag of 8 marbles, 3 red and 5 blue.  What is the probability of choosing a red marble on the 3rd draw?

If the first two marbles are not replaced after being drawn, then the 3rd draw is an example of a dependent event, because, obviously, there won't be 8 marbles in the bag when we get to the 3rd draw, there will be 6.

Dependent or not, you'll still examine the sample space of possible outcomes in either case to correctly determine the probability-it's just that the possible outcomes may be fewer than you started with.  So the dependent event changes the sample space but not how you ultimately calculate the probability.

The only comparison I can see as far as dependent and independent events are that they are both in fact events. The thing to understand is that they are different and how.

Independent events in probability will not effect the odds/probability of another event or the next event in a sequence. Where on the other hand, a dependent event is effected every time the trial/event is ran. A simple way to define the probability and discern whether an event is dependent is to make a tree diagram and see how the odds change per sequence. If they do, its dependent.