<p>Suppose that twelve different schools each have a 1/12 rate of admission. If a student applied to all 12 of them, what are his odds of being admitted to one college? Assume that each admissions decision is entirely random.</p>
<p>Bump to top.</p>
<p>Is this a serious question?</p>
<p>If you're not interested in the question, you don't need to be in this thread.</p>
<p>Okay, sorry man, it is too late to get in a tiff:</p>
<p>This is a binomial probability problem...</p>
<p>(1/12)(1/12)^11 is the answer, but you can calculate it yourself</p>
<p>Dude, get a grip</p>
<p>Is that [(1/12)(1/12)]^11, or (1/12)[(1/12)^11]?</p>
<p>Actually, that was a tyo anyway</p>
<p>It is (1/12)X(11/12)^11</p>
<p>This is a binomial probability so you multiply the probability of a sucess times the probability of a failure, however you do it to the power of number of sucesses and failure respectively...</p>
<p>It looks like this in general equation form</p>
<p>If P is probability of sucess, and Q is failure, and n is the desired number of sucesses</p>
<p>((P)^N) X ((Q)^(N-1))</p>
<p>What is this for?</p>
<p>I was just curious, really. I mean, wouldn't this be a reasonable means of predicting a student's admissions decisions? I'm aware that college admissions decisions are in no way random -- but as long as the student has test scores/GPA/ranking that put him within the right range for acceptance, using a formula like this could help him determine how many schools he needs to apply to in order to ensure acceptance to at least one college.</p>
<p>Yeah, but the guaranteed rate of sucess is so fractional, you'd report it with scientific notation. That would in no way be helpful to a student. Plus, since college admissions are NOT random, you wouldn't be able to use this. This only works if it is completely random.</p>
<p>What do you mean, fractional? I asked about the chances of being admitted to ONE college, not to ALL of them. I think the chances of being admitted to one in 12, all with the same rates of admission, should be almost 100%, right?</p>
<p>halopeno2: that's not right. you are just calculating the probability of being accepted at one and only one specific school. The correct formula would be :
where N is number of schools, P is probability of acceptance, Q is probability of failure and c represents the choose function
N c 1 * P^1 * Q ^ (N-1) + N c 2 * P^2 * Q ^ (N-2) + ... + N c (N-1) * P ^ (N - 1) * Q ^ 1 + N c N * P ^ N * Q ^ 0
This simplifies to 1 - (Q ^ N) = 1 - (11/12 ^ 12) = 0.648 or 64.8%</p>
<p>Interesting. So, this suggests that a qualified student looking at highly selective schools should plan on applying to many schools to ensure acceptance at one of them.</p>
<p>No, I gave you the answer, it is approx 3.2% chance of getting into one college. Have you ever taken statistics? The chances are awful. If you haven't taken statistics then you wouldn't understand a binomial distribution.</p>
<p>halopeno: think logically. If you have a 1/12 chance = about 8% of getting into one school when you only apply to one, it makes no sense to have only a 3.2 % chance of getting in to at least one school when you apply to 12. I showed the proper use of the binomial function, you simply calculated the chance of getting into school x and only school x (as in, accepted to only one specific school and rejected by all the others). I think that getting in to two or more schools would also fulfill what the OP wanted, which is probably the chance of getting into at least one college, not one and only one college.</p>
<p>Incidentally, if you wanted to calculate the chance of getting in to one and only one college you would have to multiply your term by the number of schools being applied to, since you wouldn't care which one accepted you.</p>
<p>You are correct, I forgot to add the coefficients to the terms. My bad, funny what no sleep and a 6 pack of Mountain Dew will do to a kid who is procrastinating doing college app stuff. Sorry about that. If you would have asked me this question on May 2, I would have gotten it right, but after APs the stuff that seems so simple starts to fade, lol.</p>
<p>Since this is not a random probability problem at all, but one directly dependent on the facts of the applicant, each school carries it's own independent probability. They are not related, so 1 in 12 remains 1 in 12.</p>
<p>I believe the OP realizes that this is not a random event, however, this problem was merely speculation on the seemingly arbitrary and logic defficient concept of college admissions.</p>