<p>If you have a 1% chance of finding a dollar and a 1% chance of getting hit by a baseball and a 1% chance of winning a scratch off lottery ticket and a 1% chance of bird poop landing in your head, the chance of any one of these happening is 4%. These probabilities are additive. (The circumstances that lead to the 1% event rates are independent.)</p>
<p>If you have a 1% chance of getting into Harvard and a 1% chance of getting into Yale and a 1% chance of getting into Stanford and a 1% chance of getting into Princeton, and you apply to all four, the chance of any one of these happing is greater than 1% but definitely not 4%. These probabilities are not additive. (Some of the “circumstances” - your own grades, test scores, essays, and recs - that lead to these 1% event rates are related / not independent)</p>
<p>Applying to more colleges increases your chances somewhat.</p>