<p>I am going to make some statements here:</p>
<p>1) The probabilities of acceptance (or rejection) to a top school are not totally independent, there is some degree of correlation between the probabilities. Also, even though the admissions committees may not talk to each other, in some cases they would be able to gauge the students attractiveness to other colleges. Washington University at St. Louis and some other schools (The Tufts syndrome) are reputed to reject candidates who they think will go a higher rated institution. Even though this causes errors (rejecting a good candidate), this could happen in any institution in individual cases.</p>
<p>2) Even with this the multiplicative approach is the correct statistical approach. Statistically the confidence interval (in laypersons terms though not really correct, the margin of error) will be very wide. Generally one would expect that multiplicative approach will lead to over stating of the results, and you will not have confidence in the results due to the introduced bias and the wide margin of error.</p>
<p>3) There is so much of subjectivity and unknowns in the admission process that one would never be able to estimate the probability itself i.e. the probability of admission itself is an estimate, which compounds the error. </p>
<p>4) Hence all you can derive from basic calculations are thumb rules. If you are in High and the medium zones (your probability of acceptance is say higher than the average, twice as high being a cut off point for those who are looking at statistical odds) it makes sense to apply to more institutions. The lower your perceived probabilities, applying to multiple institutions does not provide an noticeable advantage. This is what the OP was looking for.</p>
<p>siserune in post 172 you state that if </p>
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<p>The improvement may be marginal but it still makes sense. If you have a 90% probability of acceptance in two schools, you have 10% probability of being rejected if you apply to one school. If you apply to a second school, you drop your probability of rejection from both schools drops to 1%. Again, this is assuming a lot of the independence stuff we have talked about, but it still makes sense to apply to say two schools or three schools instead of 5 schools. If you are the 90% level applying to 5 schools as opposed to 4 schools will increase your probability marginally as you have stated. At the 20% probability of acceptance level, 5 or 6 schools may make more sense. </p>
<p>At the low level, probabilities are still multiplicative but appear to be close enough to considered additive. At 1% level applying to 3 schools increases your probability to 2.97% (close enough to 3) but in my opinion not enough to get into an ivy league. This does not mean one should not apply, it just says the odds are against you.</p>