Can someone help me on this probability question please? I'm quite comfortable with probability, but sometimes the wording of the questions REALLY throw me off. Given the following problem:

On a production line, $12\%$ of items are imperfect, and $25\%$ of these are rejected. Perfect items are never rejected. If $3$ items are selected at random, find the following probabilities:

i. The first item is rejected.
ii. No item is rejected.
The part I'm stuck at is the "$25\%$ are rejected" part. Is it:


*

*$P(I\cap R) = 0.25$ or

*$P(R\mid I) = 0.25$


Where $R$ is rejected and $I$ is imperfect.
I'm not asking for a solution to the problem. I just need help with the wording of the question.
 A: The exercise says: 12% of items are imperfect, and 25% of these are rejected. Rephrasing: given that an item is imperfect, there is $25\%$ chance that it will be rejected. So, you are given that 


*

*$P(I)=0.12$ and

*$P(R\mid I)=0.25$ 


From these you can find that $P(R\cap I)=P(I)P(R\mid I)=0.12\cdot0.25=0.03$.
A: 25% of the imperfect items are rejected.  25% of overall items are rejected makes no sense since it clearly states that perfect items are never rejected and you would necessarily reject some perfect items otherwise.  $P(R|I)=0.25$
Remember that $P(A\cap B)\leq P(A)$
$0.25=P(I\cap R)\leq P(I)=0.12$ yields a contradiction.
A: An item can vary in two dimensions: perfect/imperfect and rejected/kept.  You can draw out a 2D grid to model this:

The top-left box represents items that are perfect and kept.  The number in the bottom-right indicates items that are imperfect and rejected.  Top-right items are false-positives and bottom-left items are false-negatives.  I include row sums to the right and column sums at the bottom
Here's how to fill this in:

Let's assume we have a population of 100 items.  We're told 12% are imperfect, that's 12 imperfect items and 88 perfect items.  These are row sums.  These numbers exist irrespective of kept/rejected status.

Next we learn that 25% of the imperfect items are rejected.  This effects only the 12 items that are imperfect so we can ignore the 88 perfect items.  25% of the 12 items is 3.  The remaining 9 items are kept:


Finally, we we're told that no perfect items are rejected.  This is easy:


Now we know everything we need to answer the questions.  For our hypothetical population of 100 items, 3 are rejected.  In general, unless we know more about an item, we can say that it has a 3% chance of being rejected.  From here you should have an easier time answering your two questions.
I personally like this approach because you don't need to memorize a formula to get this far.
