The probability of being wait-listed, P(w), is half that of being admitted and 3 times as many applicants are denied than are admitted.

P(a), P(w) = 1/2P(a), P(d) = 3P(a)

$\displaystyle P(a) + .5P(a) + 3P(a) = 1\Rightarrow 4.5P(a)=1\Rightarrow P(a)=\frac{2}{9}$

However, the P(a) = .20, P(w) = .10, and P(d) = .60. What went wrong?