what is the probability that he gets at least one acceptance

I'm stuck on this question,it says:

Having endured the mental trauma that comes from taking two years of chemistry, a year of physics, and a year of biology, biff decides to test the medical school waters and sends his mcats to two colleges, X and Y. Based on how his friends have fared, he estimates that his probability of being accepted at X is o.7, and Y is 0.4. He also suspects there is as 75% chance that at least one of his applications will be rejected. what is the probability that he gets at least one acceptance.

from the given information i got
p(X) = 0.7 and p(Y) =0.4

but i can't figure out what to do from there

the probability both will reject him is [1-.7][1-.4]
probability both reject him is[.3][.6]=.18
prob. at leasrt 1 acceptance =1-.18
prob = .82 answer

Arthur

my teacher got got a different answer, he did

p(x) = 0.7 , p(y) = 0.4

p(x' U Y') = 0.75

1 -p(x intersect y)' = 0.75

p(x intersect y ) = 0.25

p(x U y) = p(x) + p(y) - p(x intersect y)
p(x U y) = 0.85

i can't figure out why the answer is not .82