difference between mutually exclusive independent
Best Results From Yahoo Answers Youtube
From Yahoo Answers
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: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: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:(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.