College admissions are not independent events

[MITer94]

The issue is that we don’t know P(A) or P(B) (I’m using A and B to mean getting into the two schools), mostly because we don’t know all the factors that go into them.

@csdad2 Exactly!

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This is one’s *credence/i, as I stated above, which is not necessarily the same as probability. Suppose I applied to colleges A and B (using ucbalumnus’ example, not knowing the requirements) with a 3.0 GPA and 27 ACT. I find out that I’m accepted by A. However my probability of being accepted to B is still zero - that is, it didn’t increase. My confidence in B likely increased, though, but I will still end up rejected with 100% probability.

This is like saying A and B don’t influence each other, but what goes into A and B are similar/related. Which again, is to say, that they’re not statistically indepedent.

The fact that A and B depend on similar information doesn’t prove they are not independent. Suppose I roll two fair six-sided dice. Define A := the first die shows 6, and B := the sum of the two dice is 7. Both A and B involve the result of the first die, but they are in fact independent:

P(A and B) = 1/36 (happens iff the first die shows 6 and the second die shows 1)
P(A) = 1/6
P(B) = 1/6