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If two events A and B are independant then P(A intersection B)=P(A)P(B)
Just take P(B) as x P(A)=3x. Apply the condition and solve for x.
phi the venn diagram i think is wrong, independant does not mean that it has no element in common.
1-P(A union B)=7/27. P(A union B)=20/27. P(A)+P(B)-P(A intersection B)=20/27. x+3x-3x^2=20/27. Solve for x.
@Phi, 15/27 is not a possible answer. Neither of you are making very much sense. I don't understand what shank means by intersection or union
yep, thanks !
Definition: Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring. Some other examples of independent events are: Landing on heads after tossing a coin AND rolling a 5 on a single 6-sided die. Choosing a marble from a jar AND landing on heads after tossing a coin. Choosing a 3 from a deck of cards, replacing it, AND then choosing an ace as the second card. Rolling a 4 on a single 6-sided die, AND then rolling a 1 on a second roll of the die. http://www.mathgoodies.com/lessons/vol6/independent_events.html
Thanks directrix. Could you give some examples of dependent then?
how can you have a union or intersection of a probability? I thought that was in sets.
Please help me.
|dw:1328149905682:dw| shankvee definitely has the right idea here
The picture means nothing to me because I have no idea what you are talking about in the first place. Please look at my last inquiry that asked what union and intersection of probability is.
Please don't give up on me. I'm getting frustrated with this problem...
maybe sat can add some insight??
I wish asnaseer was here. Do you know him?
Could you at least tell me what intersection and union are? I know what they are in sets but I don't see how it can relate to probability.
I think of it this way. You have a universe of events (that is the box) which adds up to 1 events are regions of the universe. Here's a short write up http://www.stat.yale.edu/Courses/1997-98/101/probint.htm
Here is a simple example equal number of boys and girls in school probability of selecting girl if 1/2 some students play tennis, some play chess the students who play tennis overlap with boys and girls what's the probability of choosing a student who plays chess and plays tennis a venn diagram helps you visualize the problem |dw:1328150687630:dw|
btw, prob of A occurring is 2/3
I still don't understand how that helps me. Back to the wording of the original problem; probability of a is 3x as likely as b occurring so I did a = 3b but how do i write "The probability that neither event A nor event B will occur is 7/27" in an equation so that i can do systems?
your answer is correct. but i dont see how you got it, I'm not one where drawing a picture to explain your words helps much. Sure if I have a trig problem I'll draw the triangle out, but that is just to remember what the sides or angles are in relation to one another.
what is a disjoint event, the example it gives contradicts its definition because it says when two events have no outcomes in common the events are disjoint, but the example it gives only has one event and it says it is disjoint. To what?
"neither event A nor event B will occur is 7/27" means that A, B, or both occur 20/27 times Prob (A) + Prob(B) - Prob( both A and B) = 3b + b - b*3b where the x*3x comes from the statement that A and B are independent. As pointed out above, independent means Prob(A and B) = P(A)*P(B)= 3b*b= 3b^2
we subtract Prob(both A and B) because we would be double counting if we don't
so does P(A) + P(B) = 20/27?
almost. if your were counting tennis players and chess players it would add up correctly. But if someone plays both chess and tennis you have to subtract the double counting. so Prob (A) + Prob(B) - Prob( both A and B) = 20/27
I see. And the probability of A and B is like saying what is the probability of this happening and then this happening. So it would be mutliplication of the two probabilities?
yes. I think events are "randomly pick" out of the universe. what's the probability of selecting something out of the A box or B box. And somethings can be in both.
so say 1/4 prob. of someone in chess, and 1/5 prob. someone in tennis you would do 1/4 + 1/5 = 9/20 - 1/20 = 8/20?
if they are independent, which is a reasonable assumption.
what about if they were dependent, how would that change, what does that really even mean?
Dependent means the probability of event B changes (depends) on event A occurring
so now we have P(A) = P(3B) and P(A or B) - P(A and B) = 20/27 right? This is the same as P(3B or B) - P(3B and B) = P(3B) + P(B) - P(3B^2) = 20/27 Where do we go from here?
3B^2 - 4B + 20/27 = 0?
With that we get 10/9 and 2/9. 10/9 is impossible so it has to be 2/9 which is the probability of B occurring. Since A = 3B then A = 3 x 2/9 = 6/9 = 2/3!!!!!! I got the answer!!! Thank you thank you thank you thank you!
thanks, but I'm learning this too...
what do you mean?