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Example:Finding Probability of Independent events

 Post to:   Explanation:

Independence (probability theory)

In probability theory, to say that two events are independent intuitively means that the occurrence of one event makes it neither more nor less probable that the other occurs For example:

1.  The event of getting a 6 the first time a die is rolled and the event of getting a 6 the second time are independent.

2.  By contrast, the event of getting a 6 the first time a die is rolled and the event that the sum of the numbers seen on the first and second trials is 8 are not independent.

3.  If two cards are drawn with replacement from a deck of cards, the event of drawing a red card on the first trial and that of drawing a red card on the second trial are independent.

4.  By contrast, if two cards are drawn without replacement from a deck of cards, the event of drawing a red card on the first trial and that of drawing a red card on the second trial are again not independent.

Similarly, two random variables are independent if the conditional probability distribution of either given the observed value of the other is the same as if the other's value had not been observed. The concept of independence extends to dealing with collections of more than two events or random variables.

In some instances, the term "independent" is replaced by "statistically independent", "marginally independent", or "absolutely independent".

## Independent events

The standard definition says:

Two events A and B are independent if and only if Pr(A  B) = Pr(A)Pr(B).

Here A  B is the intersection of A and B, that is, it is the event that both events A and B occur.(Our solved example in mathguru.com uses this concept)

http://en.wikipedia.org/wiki/Independence_(probability_theory)#Independent_events