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# Probability watch

1. James has applied to 2 different universities. The acceptance rate for applicants with similar qualifications is 25% for University X and 40% for University Y. What is the probability that James will be accepted at least by one of the two universities?

I have been unable to work out a method to solve the above. Can anybody help me out? At the moment I am leaning towards the idea that I might have to add both probabilities and subtract the probability that both will accept simultaneously so: .40 + .25 - .1 = 0.55 but I am pretty sure this is not correct. Any help would be much appreciated.

EDIT:
There is only one other question I am struggling with:
Suppose P(A)=.45, P(B)=.20, P(C)=.35, P(E|A)=.10, P(E|B)=.05 and P(E|C)=0. What is P(E)?
I don't understand how I can get P(E) with this information.
2. Anyone?
3. 0.55 is correct. Alternatively: P(will be accepted by either) = 1 - P(will be rejected by both) = 1 - 0.6 * 0.75 = 0.55

The law of total probability gives P(E) = P(E|A)P(A) + P(E|B)P(B) + P(E|C)P(C) (check that P(A) + P(B) + P(C) = 1).
4. (Original post by Glutamic Acid)
0.55 is correct. Alternatively: P(will be accepted by either) = 1 - P(will be rejected by both) = 1 - 0.6 * 0.75 = 0.55

The law of total probability gives P(E) = P(E|A)P(A) + P(E|B)P(B) + P(E|B)P(B) (check that P(A) + P(B) + P(C) = 1).
Thanks alot. So how would P(E) be worked out? You add P(E|B)P(B) twice as you have said?
5. (Original post by IsThisLife???)
Thanks alot. So how would P(E) be worked out? You add P(E|B)P(B) twice as you have said?
Sorry, I made two independent typos each with probability 1/3 (lol). It's edited; it should be P(E|C)P(C) as the last term.
6. (Original post by Glutamic Acid)
Sorry, I made two independent typos each with probability 1/3 (lol). It's edited; it should be P(E|C)P(C) as the last term.
lol I thought so.
So for my question: (0.45 * 0.1) + (0.2 * 0.05) + (0 * 0.35) which is 0.045 + 0.01 which adds up to 0.055?
Also a quick general question. Doing my A levels I never touched Statistics. I only did Mechanics 1 & 2. One of my Uni modules includes statistics so this is all new to me therefore I am interested in your opinion on how difficult Statistics is and how easy it is to grasp?
7. (Original post by IsThisLife???)
lol I thought so.
So for my question: (0.45 * 0.1) + (0.2 * 0.05) + (0 * 0.35) which is 0.045 + 0.01 which adds up to 0.055?
Also a quick general question. Doing my A levels I never touched Statistics. I only did Mechanics 1 & 2. One of my Uni modules includes statistics so this is all new to me therefore I am interested in your opinion on how difficult Statistics is and how easy it is to grasp?
Hmm, I find that probability is something in which not a huge amount of knowledge is needed, and indeed computing probabilities can reduce to elementary counting arguments and the like. Not to say that this is easy, just that the tools required to solve probabilistic questions at university may require no more mathematical tools than what one would have at GCSE. So, if one is to become proficient in probability / statistics, the best idea is that once one is acquainted with the theory is to delve into problems. For familiarizing yourself with such problems will allow you a feel for what should work and what shouldn't work, whether one can assume something or whether one can't; it will allow an intuition. In maths, we try to reduce an unsolved problem into a problem we know how to solve, and doing more problems creates more ways of actually reducing the problem. So, in summary: I think statistics can be pretty damned difficult, one can stare for hours at a question which can be tied up with an elegant and beautiful one line solution, but compared other areas of maths the theory itself is compact and not too difficult to grasp.

[Note I've referred more to the probabilistic side of statistics.]
8. (Original post by Glutamic Acid)
Hmm, I find that probability is something in which not a huge amount of knowledge is needed, and indeed computing probabilities can reduce to elementary counting arguments and the like. Not to say that this is easy, just that the tools required to solve probabilistic questions at university may require no more mathematical tools than what one would have at GCSE. So, if one is to become proficient in probability / statistics, the best idea is that once one is acquainted with the theory is to delve into problems. For familiarizing yourself with such problems will allow you a feel for what should work and what shouldn't work, whether one can assume something or whether one can't; it will allow an intuition. In maths, we try to reduce an unsolved problem into a problem we know how to solve, and doing more problems creates more ways of actually reducing the problem. So, in summary: I think statistics can be pretty damned difficult, one can stare for hours at a question which can be tied up with an elegant and beautiful one line solution, but compared other areas of maths the theory itself is compact and not too difficult to grasp.

[Note I've referred more to the probabilistic side of statistics.]
OK, I guess you are right. I am doing pure Economics but involves a couple of modules which involve Statistic analysis in Economics. At the moment we are looking at probability, variance, standard deviation etc. Hopefully it wont become too stimulating but you are right, I should familiarize myself with problems and their solutions. Thanks.

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