If somebody could please help me...

<p>I am having difficulty comprehending the reasoning of a certain question in the Barron's book. The final probability chapter question in the final section of the book (2008 edition: question about 80% good items 20% defected etc..)
I do not understand if at first you select 8 items and then 5 out of those, or why can there only be 5 good items, or not - I have no idea, no matter how I try I cannot comprehend the syntax of the question, and thus have no idea why the answer involves combinations. I would also like to ask the people who have taken the test or who are familiar with the format, of how likely such a question as: given the sequence 2,x,y,9 and the first 3 are part of arithmetic sequence and last 3 are geometric and so please find the possibilities for x and y - how likely is this to come up (there are at least 12 things you must do to answer this and yet barron's uses it as an example? - I understand this one but I am a little bit firghtened)
Thank you very much, if someone could please answer both questions (or one person answers one and somebody else another)</p>

<p>If you didn't know, Barron's tests are ridiculously harder than the real SAT II, especially for Math IIC. If you find yourself stuck almost everytime, then I suggest you find another book like Princeton Review.</p>

<p>Other than that, I can't figure out what you are trying to say.</p>

<p>I understand that, but usually solving complex barron's problems + understanding them helps solve much easier problems and boosts confidence, I have PR. The reason you can't understand what I am trying to say is because I have not written down the question, (I just waitied for someone with the book to help) I will write down the question now:</p>

<p>If a box contains 80% good and 20% faulty items, what is the probability of obtaining exactly 5 good items out of 8 randomly selected items.</p>

<p>Answer Explanation: We must assume infinity. The chances of getting 5 good items ( and thus 3 bad items ) is (0.8)^5(0.2)^3 and there are (combination parenthesis) (5(out of) 8) ways of doing this. Thus answer is 0.8^5 * 0.2^3 * (the number of combinations of selecting 5 out of 8 objects).</p>

<p>I am slowly starting to understand this, but I just put my thoughts on this clearly - if someone could please help me...</p>

<p>Well you are selecting 8 random items.
you want 5 good ones, which have a 80% chance of occurring.
you also need 3 bad ones, which have a 20% chance of occurring.</p>

<p>Good items: (.8)^5, because there are 5 items and each item has a 80% chance, if you don't understand (.8)^5, then u might understand if I write it like this, .8 x .8 x .8 x .8 x .8</p>

<p>same goes for the bad items, there are 3 items with a 20% chance, .3 x .3 x .3</p>

<p>Remember you want both of these to occur, so you multiply.
tell me if you don't understand.</p>

<p>and btw, why would you wait for someone with a book to help you? I also have Barron's book, but I wouldn't spend ~10 minutes looking through the book to find the problem you are talking about.</p>

<p>Thank you for trying - but notice that I said that in the explanation you FURTHER multiply the 0.8^5 * 0.2^3 BY THE NUMBER OF WAYS SELECTING 5 OUT OF 8 THINGS ( 8 nCr 5) </p>

<p>so
0.8 0.8 0.8 0.8 0.8 0.2 0.2 0.2 ( 8 nCr 5 ) = the answer</p>

<p>I am starting to get this clear in my head, but perhaps someone can help</p>

<p>There's never anything this hard on the SAT... I wouldn't even bother putting the effort into figuring it out if I were you.</p>