Conditional probability question with set theory things

[zeion]

Homework Statement

Basically, I'm given the probability of 4 independent events:

P(A) = 0.04
P(B) = 0.03
P(C) = 0.02
P(D) = 0.01

If anyone of these occur, a failure will happen.
More than one can happen at the same time.

I need to find the probability that more than one of them has occurred given at least one as occurred.

Homework Equations

The Attempt at a Solution

I solved for the prob that at least one occurred:
Let F = A∪B∪C∪D
Then P(F) = P(A) + P(B) + P(C) + P(D) - P(A∩B∩C∩D) = 0.09999976

Now I have to solve for prob of 'more than one' occurred given F has occurred.
I'm stuck on this part.
How do I represent 'more than one occurred' with symbols?
Would it be E = (A∩B)∪(A∩C)∪(B∩D)∪(C∩D)?

Then P(E | F) ?

 

[zeion]

No one..?
Is my post not understandable?