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difference between mutually exclusive independent
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Question:The definition of Mutually exclusive events: 2 events are mutually exclusive if the ocurrence of one event precludes the ocurrence of other event
Independent Event: 2 events are independent if the ocurrence of one event in no way influences the probability of the ocurrence of the other event
ISN'T THIS THE SAME? I DOn't understand the diff. between mutually exclusive and independent events! help plz :( try to use examples if u can, thanks
Answers:If A and B are mutually exclusive events then P(A U B) = P(A) + P(B) and P(A B) = 0, because the intersection of A and B is the empty set, i.e., A B = . Two events are independent if: P(A  B) = P(A), this implies that P(A B) / P(B) = P(A) and thus P(A B) = P(A) * P(B) If A and B are mutually exclusive then P(A B) = 0 and P(A  B) = 0. This shows that mutually exclusive events A and B are not independent given P(A) > 0 and P(B) > 0. Examples: Roll two dice, let A be the event that both dice show a 1, 2, or 3. Let B be the event that the sum of the to dice is greater than 7. A and B are mutually exclusive because it is impossible for both events to happen at the same time. The are not independent because if A happens you know that B cannot happen. Knowing something about one of the events tells you about the other.
Answers:If A and B are mutually exclusive events then P(A U B) = P(A) + P(B) and P(A B) = 0, because the intersection of A and B is the empty set, i.e., A B = . Two events are independent if: P(A  B) = P(A), this implies that P(A B) / P(B) = P(A) and thus P(A B) = P(A) * P(B) If A and B are mutually exclusive then P(A B) = 0 and P(A  B) = 0. This shows that mutually exclusive events A and B are not independent given P(A) > 0 and P(B) > 0. Examples: Roll two dice, let A be the event that both dice show a 1, 2, or 3. Let B be the event that the sum of the to dice is greater than 7. A and B are mutually exclusive because it is impossible for both events to happen at the same time. The are not independent because if A happens you know that B cannot happen. Knowing something about one of the events tells you about the other.
Question:
Answers:Not necessarily. If I go to the grocery store, and you go to the grocery store, those events are independent. However, they could happen at the same time, or, we could even go to the grocery store together.
Answers:Not necessarily. If I go to the grocery store, and you go to the grocery store, those events are independent. However, they could happen at the same time, or, we could even go to the grocery store together.
Question:Two mutually exclusive events having positive probabilities are_____dependent
A. Sometimes
B. Always
C.Never
Explain why pls!
Answers:Sounds like a trick question. If they are mutually exclusive events, they never coincide, one event precludes the other from happening. ( I think, been a while since I studied stats so best to review your glossary). However, if something's probability is 1 on a scale from 0 to 1, it IS going to happen. So one the one hand they are dependent, on the other hand they are independent. I would go with answer D: "Your questions are all f***ed up. "
Answers:Sounds like a trick question. If they are mutually exclusive events, they never coincide, one event precludes the other from happening. ( I think, been a while since I studied stats so best to review your glossary). However, if something's probability is 1 on a scale from 0 to 1, it IS going to happen. So one the one hand they are dependent, on the other hand they are independent. I would go with answer D: "Your questions are all f***ed up. "
Question:consider families with two children,assuming equal probability for both genders.Let A be the event that chosen family has at most one boy,B be the event that the chosen family has a boy and a girl and C be the event that either the chosen family has two boys or two girls.
(a) calculate P(A),P(B) and P(C).
(b) is P(AB) = P(A)P(B)? are A and B independent?are they mutually exclusive?
(c) is P(BC) = P(B)P(C)? are B and C independent?are they mutually exclusive?
however,prove that if A and B are independent events and P(A)> 0 and P(B) > 0,then A and B must be not mutually exclusive. (A very simple proof consists of one line only!)
Answers:(a) P(A) = 75% P(B) = 50% P(C) = 50% The first is due to the fact that they could only achieve the opposite 25% of the time, if they had two girls. The second is due to the fact that there's a 50/50 chance that the second child's sex is opposite that of the first. The third works the same way  there's a 50/50 chance that the second child's sex matches that of the first. (b) A and B are not independent, nor are they mutually exclusive. If B happens, A must have already happened. Thus: P(AB) = P(B) = 50% Note that P(AB) is the probability that A and B happen, often also written P(A B). There is also the probability that A or B happens, P(A+B)=P(A B), which we don't consider in this problem. (c) The two events are mutually exclusive. The two children cannot simultaneously have the same sex and have the opposite sex. Thus: P(BC) = 0 (d) For two independent events A and B, with P(A)>0 and P(B)>0, we know P(AB)=P(A)P(B)>0. Hope that clears it all up.
Answers:(a) P(A) = 75% P(B) = 50% P(C) = 50% The first is due to the fact that they could only achieve the opposite 25% of the time, if they had two girls. The second is due to the fact that there's a 50/50 chance that the second child's sex is opposite that of the first. The third works the same way  there's a 50/50 chance that the second child's sex matches that of the first. (b) A and B are not independent, nor are they mutually exclusive. If B happens, A must have already happened. Thus: P(AB) = P(B) = 50% Note that P(AB) is the probability that A and B happen, often also written P(A B). There is also the probability that A or B happens, P(A+B)=P(A B), which we don't consider in this problem. (c) The two events are mutually exclusive. The two children cannot simultaneously have the same sex and have the opposite sex. Thus: P(BC) = 0 (d) For two independent events A and B, with P(A)>0 and P(B)>0, we know P(AB)=P(A)P(B)>0. Hope that clears it all up.
From Youtube
Mutually exclusive vs. independent :In this video I discuss the difference between the probabilistic concepts of mutual exclusive and independent events.
Excel Finance Class 75: IRR and Mutually Exclusive Projects  Plot Chart To See Cross Over Rate :Download Excel workbook people.highline.edu Learn about : IRR and Mutually Exclusive Projects. Build a table and plot an XY Scatter chart to see that at different Required Rates of Return we get different Net Present Value amounts with Mutually Exclusive Projects. Build a table of Difference Cash Flows to then calculate the cross over rate.