Anyone good at math (statistics) want calculate probabilities?

Colleges and Universities A-Z California Institute of Technology
1

<p>I guess I will begin. What are the probabilities (purely mathematical chances-not considering stats assuming that ones in the average range of each school) of being admitted to at least one school if the average acceptance rates are as follows:</p>

<p>35.2
28.0
23.3
9.2
23.0
26.8
21.4</p>

<p>I listed 7 schools. I got admission statistics from USNEWS: National Universities Rankings - Best Colleges - Education - US News and World Report</p>

<p>So if some one can calculate my probability of getting accepted to one school that would be greatly appreciated. Also if you're really good at math than the probability of being accepted to two schools.</p>

<p>Also feel free to post the schools and their admission rates you guys applied to and I'm sure someone on this forum would calculate your probability of being accepted to at least one school.</p>

<p>If anyone can provide a general formula that would be really nice too. Thanks a lot. If possible can you guys provide the most accurate probability like not assuming independence if that's possible.</p>

2

<p>You already got the answer in the other forum, which assumes that the decisions are independent (they aren’t). There’s no way to treat the probabilities as anything other than independent unless you know what the dependence is. In other words, you’re trying to shrink something incredibly complicated into a statistic based on one number. Any number someone will be able to give you from this will be meaningless.</p>

3

<p>Just rubbing salt in the wounds aren’t you. I just got wrecked by the math 2b (stats and probability) final.</p>

<p>On that note, they’re obviously not completely independent, and there’s no way to calculate the dependence. But assuming independence, is rather easy to figure out the probability of getting into at least one school; just take the one minus the product of one minus each of the probabilities, which results in a 85.605% chance of being admitted into at least one of the schools. But that number is pretty meaningless for reasons stated above.</p>

<p>I could do the other probabilities you asked, but they’re fairly computation intensive, and frankly, it’s not worth it.</p>

4

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</p>

<p>Because we’re here just to do your pointless math problems.</p>

5

<p>class2009college: So I’m no mathematician, but I can bang stuff in on a keyboard and watch it run. So I wrote a program which simulates the college admission process in the following manner–it converts the admit % from the 0-100 scale to a 0-1 scale by cleverly dividing by 100; then it generates a random number on [0, 1), and if this number is lower than the admit %, YOU’RE IN!!! I then proceeded to iterate this process 100,000,000 times (“computer abuse!” you may cry…but that’s okay, it’s on a computer in my house’s comp lab, not my own computer. =)). Here is a copy of the output from the program:</p>

<p>Chance of getting into exactly 7 of the listed schools under the ridiculously flawed assumption of independence: 0.002861%
Chance of getting into at least 7 of the listed schools under the ridiculously flawed assumption of independence: 0.002861%</p>

<p>Chance of getting into exactly 6 of the listed schools under the ridiculously flawed assumption of independence: 0.076037%
Chance of getting into at least 6 of the listed schools under the ridiculously flawed assumption of independence: 0.078898%</p>

<p>Chance of getting into exactly 5 of the listed schools under the ridiculously flawed assumption of independence: 0.831266%
Chance of getting into at least 5 of the listed schools under the ridiculously flawed assumption of independence: 0.910164%</p>

<p>Chance of getting into exactly 4 of the listed schools under the ridiculously flawed assumption of independence: 4.796589%
Chance of getting into at least 4 of the listed schools under the ridiculously flawed assumption of independence: 5.706753%</p>

<p>Chance of getting into exactly 3 of the listed schools under the ridiculously flawed assumption of independence: 16.018344%
Chance of getting into at least 3 of the listed schools under the ridiculously flawed assumption of independence: 21.725096999999998%</p>

<p>Chance of getting into exactly 2 of the listed schools under the ridiculously flawed assumption of independence: 31.14194%
Chance of getting into at least 2 of the listed schools under the ridiculously flawed assumption of independence: 52.867036999999996%</p>

<p>Chance of getting into exactly 1 of the listed schools under the ridiculously flawed assumption of independence: 32.736359%
Chance of getting into at least 1 of the listed schools under the ridiculously flawed assumption of independence: 85.603396%</p>

<p>Chance of getting into exactly 0 of the listed schools under the ridiculously flawed assumption of independence: 14.396604%
Chance of getting into at least 0 of the listed schools under the ridiculously flawed assumption of independence: 100.0%</p>

<p>huzzah!</p>

<p>I’d like to thank you, class2009college, for giving me yet another excuse to avoid my hum final essay. I’ve now been on a break for the last six hours straight. Woo!</p>

6

<p>That’s what you were using that computer for?</p>

<p>Thanks for letting me check my e-mail.</p>

7

<p>Of course. I hope I didn’t give you the false impression that I was being productive in any way. Productivity and I haven’t really gotten along lately.</p>

8

<p>

</p>

<p>Really? Monte carlo? You can write brute force really quickly and it’s tractable for n = 7:</p>

<p>


</p>

<h1>include <iostream></iostream></h1>

<p>using namespace std;</p>

<p>double prb[] = {.352, .28, .233, .092, .23, .268, .214};
int N = 7;</p>

<p>int main() {
  double ret[N+1];
  memset(ret, 0, sizeof(ret));
  for (int i = 0; i < (1 << N); ++i) {
    int j = i, schools = 0;
    double p = 1;
    for (int k = 0; k < N; ++k, j/=2) {
      if (j % 2) {
        schools++;
        p *= prb[k];
      } else {
        p *= (1.0 - prb[k]);
      }
    }
    ret[schools] += p;
  }</p>

<p>for (int i = 0; i <= N; ++i) {
    cout << "ridiculously flawed prb of exactly " << i << " is " << ret* << endl;
  }
}

</p>

<p>output
$ ./srslywhat
ridiculously flawed prb of exactly 0 is 0.14395
ridiculously flawed prb of exactly 1 is 0.327385
ridiculously flawed prb of exactly 2 is 0.311374
ridiculously flawed prb of exactly 3 is 0.160212
ridiculously flawed prb of exactly 4 is 0.0479807
ridiculously flawed prb of exactly 5 is 0.00830908
ridiculously flawed prb of exactly 6 is 0.000761542
ridiculously flawed prb of exactly 7 is 2.7869e-05</p>

9

<p>I’m tempted to pay off some poor high school kid to post here now, listing the 30+ schools he applied to…<em>then</em> we’ll see how your brute force does, foul demon!</p>

<p>(pay no mind to the fact that the accuracy of mine would also likely degrade to unacceptably poor levels)</p>