SOLUTION: Suppose Q and S are independent events such that the probability that at least one of them occurs is 1/3 and the probability that Q occurs but S does not occur is 1/9. What is th

Draw a Venn diagram with two sets, Q and S.  There are 4 regions
for the four possibilities:

Let w = P(Q occurs and not S does not occur)
Let x = P(Q occurs and S occurs)
Let y = P(S occurs and Q does not occur)
Let z = P(Q does not occur and S does not occur)

We put the 4 letters in the corresponding regions:

 
That is the part of the red circle Q that is not part of the blue
circle, the left part of the red circle Q. So w=1/9. So we put
1/9 in place of w.

Therefore we have the equation:

Since the probability of S is x+y, we can determine that by
solving for x+y:

  <--answer

[We have the answer already. We did not need to use that they are independent.
In fact as it turns out, they could NOT be independent!!]

Edwin