<p>Okay, now if we did assume that acceptance to each school is a totally dependent event, than the overall acceptance rate would be about 35%. However, if they’re all independent events, then the probability of acceptance at at least one school is 1 - (probability of being rejected at all schools). </p>
<p>The probability of getting rejected everywhere is: </p>
<p>.81 * .66 * .65 * .86 * .66 = .19, making the overall acceptance rate about</p>
<p>81%. Unless there is an inverse correlation between acceptances at different schools (highly unlikely IMO), that seems to be the highest overall acceptance rate. </p>
<p>Now, unless people really don’t apply to all 5 schools that they can, the overall acceptances should lie between 35% and 81%. </p>
<p>Last year I did some statistics on the MIT regular decision board, and found that the admissions percentage was about 50% for people who had posted. Clearly CC is not a random sample, and clearly there is a reporting bias in favor of those who are accepted. </p>
<p>So it’s very much a statistical possibility that the mail orderings really are random (as has been said by the admissions office on numerous occasions), and that we’re really just starting a crazy conspiracy theory.</p>
<p>he probably took AP statistics or something…it really isn’t that hard, but where he draws his conclusion about how many people may or may not have applied to all three schools is too unknown to make a good guess. Where does he get his margin of error too? If he performed a hypothesis test, there are certain conditions that must be met such as simple random samples, etc…</p>
<p>If everyone applied to all 5 schools and the adcom picked randomly out of a hat, then the above may be the case. Reality is that not everyone applies to more than 5 schools, and many that apply to more than one get accepted to more than one. Also, many will be rejected by all, because admission is not random (as much as some people believe it is ).</p>
<p>I take the independence/dependence of decisions into account. If they’re 100% dependent (i.e., getting admitted to SCS means 100% chance of admission to Tepper), then yes, that would be true. There’s be an overall acceptance rate of 35%. If they’re all independent, then it would be 81%. It’s probably somewhere in between those two numbers, and I wouldn’t be able to figure it out without serious number crunching, which I’m too lazy, and don’t have the unbiased sample statistics to do. </p>
<p>I took statistics at the community college, but honestly someone could probably do this without a dedicated statistics course.</p>
).</p>