<p>OK, here are some of my final thoughts on this question. But before I discuss its solution (or what I think is the solution) we need to demystify two things. First, on the subject test, test questions are NOT arranged in order of difficulty. This is true many times over. Although there are many hard questions towards the end, there is also a fair share of easy and medium ones. My october administration of math 2 (which was a makeup adminsitration so it will different from what u guys took) had a very easy solid geometry question at its end (#50). Second, the subject tests ARE NOT not a measure of reason as much as they are a measure of specific knowledge. We need to keep this in mind when considering question #49. It is not necessarily true that that question was hard, nor was it true that it needed serious internal debate inside the mind test-taker as to whether or not the order of the events mattered. CB claims that the test questions are fair and one of their definitions of fair is that all questions have clear and explicit instructions. Now we need to remember that the SAT does not measure very advanced statisitics and actuaries, and the level of knowledge of probability is not that hard. In fact, majority (about 90%) of the probability questions are quite easy if you study them before the test. One could make a list of all the types of probability questions - order no order, permuations or combinations, intersection, mutually inde..., etc. Therefore it is not wrong to assume that CB simply wanted to measure the test-takers knowledge of independent events and we should also agree - as stated before - that this was not necessarily a hard question. Even if it were, there is another point in question. If you wanted to measure someones writing ability, you dont have to ask him to write about every single topic because testing writing skills is like testing a blood sample - wherever you take the sample from, it is invariably the same. This however does not hold true for the math subject test. It is not wrong to say that the test makers try to make the test as "comprehensive" as possible. Of course, certain topics are not always tested; for example this test did not include imaginary and complex numbers among other things. However CB still tries to make the test comrpehensive, because the aim of the test is to measure specific knowledge. And here arises an interesting point. If you refer back to the test, you will remember that there were three probability/counting questions. One was on the samples and I think we all unanimously agreeed on its answer and so did we on the "sum = 7 question - it's answer was 0.06" Now the sum question tested our understanding of the importance of order and the sample one tested knowledge of difference between combinations and permutations etc. If the phone call question did require us to factor in order when we calculated the probability, then that would have made it almost the same as the sum question. The fact that the question did not specify whether or not order was an issue must mean that CB assumed it was obvious. But this thread suggests otherwise. Another thing is that when independent events are combined in some way as in the case of the dice ( we want the sum to be a certain number) order matters. But when the events are not combined and are looked at as a whole, then order does not matter as in the case of the phone calls. Imagine a hypothetical situation: I am a customer subscirbing to "the telephone company". The company tells me, cost of a local call is $1/min, cost of a int'l call is $3 and a local call "linked" to a int'l call is $2. At the end of the month I receive my bill. There will be a section for local calls, int'l calls, and for linked calls. I'm pretty sure that the bill wont sepcify order.</p>
<p>Keeping all of this in mind, I think its safe to assume that order did not matter for the phone call question. An interesting observation is that this particular question is - as you all have so astutely noticed - is in fact question #49. Take the number 49 and insert a forward slash between 4 and 9 and you get fraction -four by nine-!!!........ "The College Board code" maybe, maybe not ;)</p>
<p>I'm looking at the argument, and I'm still wondering if anyone is 100% sure about the question. What was the wording? It DEFINITELY said 'either'? I recall just an 'and' when I try to remember. And I remember it said independent events as well...</p>
<p>im very glad you think that order does not matter. however order doesnt always mean less probability. sometimes order means more possible outcomes. for example. i want to eat a meal. for me, eating main course then dessert is different than eating dessert then main course. here there are more possible outcomes hence a higher probability. if i said order didnt matter then the possible outcomes are less. the same applies to the calls. i dont care about order as long as both types happen, that means less ways to make the calls, meaning a lower probability. order affects the probability of an event depending on the logic of the situation. so im guessing now its 2/9 ehm ehm.... ;)</p>
<p>you want to eat a meal and order doesn't matter to you
so you got 2 possibilities of eating: dessert and main then course OR main course then dessert </p>
<p>but, no you want to eat main course then dessert, so possibility is only 1.</p>
<p>Did you have prob lessons? Didn't you do experiment with coin?
If no, try it now. Throw 2 coins about 50 times, and you'll see, that it comes about
25% 2 heads
25% 2 tails
50% tail and head</p>
<p>first, that was just an example. second theres a difference between empirical probability and statistical probability. i dont need to throw a coin 50 times to get a 50:50 chance for heads and tails, for all i know it could land 50 times as "heads". finally order doesnt always means less probability. u say its 4/9 and not 2/9 because no order means less probability. well supposing there was a mistake in the booklet and instead there was 3/9 and 7/9. would you have picked 7/9 just because it signified higher probabiltiy? now supposing im making a 4 digit code. and order of digits doesnt matter. 1234 would be the same as 2314. here no-order means less ways of creating codes, but to a hacker it means more chances of cracking it. like i said it depends on the logic of the situation. with the phone again, order a u said and as i have said, did not matter. and so it seems that it translated into a less probability.</p>
<p>empirical probability and statistical probability</p>
<p>what?! no, there is no difference. yes, it could be 50 times 2 heads, but probability of that situation is 0.25^50, so, let's say, small.</p>
<p>And I know very well what I am doing, the way of getting answer is shown in #1 post.</p>
<p>On our secondary leaving exam, we are getting point not for pure answer but for way of getting it. I know how to make every probablistic task mathematically, with describing sample space and events in that sample space. If you wish, I can do it for you and you can just put this into c++ compilator and your computer will count this for you, babe.</p>
<p>well, this is the SAT not ur school leaving exams, u only need to put in "A,B,C,D,E" on the answer sheet. ur crusing around the million dollar questions 1) does order matter? no, good we agreed on that? 2) is probability less or more. well i say less. why? as i showed you in my previous example. with no order u can make the calls under the specified condition in two ways- local then int'l or int'l then local. but since order doesnt matter they count as one. statistical (theoretical) probability is the same as empirical??!!! wow. good news for investment companies and bad news for casinos. and i guess people should stop saying good luck to each other.......
ur sample space in post 1 is wrong. there u have three events not two G, U, L this is a correct one and let everyone tell u this the classic/right way</p>
<p>events : Local (L) international (I)</p>
<p>1) L-L
2) L-I
3) I-I
4) I-L </p>
<p>as you can see such a sample space wouldn't help much becuase here you have to calculate the probabiltiy of all the individual events. while on the question u are given the probability of the desired events. and they are independent too.</p>
<p>sample space is not 2 but 9.
We have set of 3 events (1 local, 2 international), from which 2 happened. Mathematically it's called variation and expressed by V=n^k, where n is number of elements in basic set, and k nuber of elements in set B buit from A-set elements.</p>
<p>mathematically, it looks like</p>
<p>A={w=(x1,x2):x1,x2E~{1,2,3}} I used E~ as "is subset"</p>
<p>and, everything could happen, of course, but if you'll throw 2 coins 1000 times, you'll get something like 25.087376837% etc, if you'll throw 10000000000 times, you'll get 25.00000006727% etc. And haven't you noticed that you could win more when probability is less?</p>
<p>simply wrong. only two events. theres no need for subsets and sophisticated equations. the answer is 2/9 if ordered mattered it will be 5/9. if we agreed that order did not matter then it confirms that the answer is 2/9. look at the difference between my arguments and yours. everytime u just come up with a new technique that proves nothing. i on the other hand explore the whole scenario from all possible viewpoints. the material that is required for the sat 2 is simply this. intersection independent probabilties/evens is the product of the respective Ps. if order mattered we would have thrown in a x2 in there but since you agreed its not about order well then know in your heart that the answer is 2/9 :)</p>
<p>Of course. I think that we should end our discussion at this point. Have you read don kichot? It is not even real to change the way of thinking of person having his or her own world. You can think about me in that way too, if you wish.</p>
<p>To settle this, I'm almost positive that the answer is 2/9. Here's why: I omitted 3. I also know for sure that I got the following 3 wrong:</p>
<p>-Compound interest I did it wrong because I compounded it 4 times instead of doing it quarterly.
-The graph question I guessed the only choice with a=0, the rest was like b=c, d=..., and I know that it was wrong.
-The samples in the lab I put 1820 or something because I forgot to multiply by 4.</p>
<p>That is a total of -7 for sure, and a raw score of 43. Since I got an 800, then I'm guessing the curve had to be -7 = 800. So assuming they didn't make the curve super easy at -8 or something, I must have gotten all the other questions right, and I put 2/9 for the long distance question, so that has to be right, right?</p>
<p>I highly doubt that. I haven't ever heard of the curve being a -8 before, and this test was definitely not hard enough to warrant that big of a curve.</p>