Mutually exclusive events vs Independent events
In regards to probability, are Mutually exclusive events the same as Independent events?
If not, how are they different?
Events [tex]A[/tex] and [tex]B[/tex] are mutually exclusive if [tex]A \cap B = \emptyset,[/tex] which means they cannot both occur. Those events are independent if [tex]P(A \cap B) = P(A)P(B),[/tex] which means one occurring does not affect the other occurring.
If [tex]P(A) > 0[/tex] and [tex]P(B) > 0[/tex] then those events cannot be both mutually exclusive and independent. This is because mutually exclusive implies [tex]P(A \cap B) = 0[/tex] while independence implies [tex]P(A \cap B) = P(A)P(B) > 0.[/tex]
mutually exclusive events have no outcomes in common.
ex: probability of rolling doubles or a sum of 6 with two dice?
these events are not mutually exclusive, cause you can roll a 6 with two 3's, which are also doubles. you solve this by adding the probability of rolling doubles (6/36) with the probability of rolling a sum of 6 (5/36) and then taking away the outcome in common (1/36) answer is .27
ex: probability of rolling doubles or an odd number?
these events are mutually exclusive because there are no events in common. you solve this by adding the probability of rolling doubles (6/36) with the probability of rolling an odd number (18/36). answer is .66
"Two events are said to be independent if the result of the second event is not affected by the result of the first event."
http://www.mathgoodies.com/lessons/vol6 ... vents.html
google is your friend for generic questions
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