We are looking for the probability that
exactly one pen is defective. There are 3 options for what we could get in the box
- Exactly one defective pen
- More than one defective pen
Because there is a 100% probability that we will get one of the options above, this means that the probability of each answer choice added together should equal 100%:
% chance of no defective pens + % chance of exactly one defective pen + % chance of more than one defective pen = 100%
So if we know the % chance of no defective pens AND the % chance of more than one defective pen, we can solve.
Statement 1 only tells us the % chance of no defective pens - we don't know the % chance of more than one defective pen. Insufficient.
Statement 2 only tells us the % chance of more than one defective pen - we don't know the % chance of no defective pens. Insufficient.
Both statements together give us % chance of no defective pens AND the % chance of more than one defective pen, so we should be able to solve. Sufficient. We don't need to do the math, but if we did, we would get:
% chance of no defective pens + % chance of exactly one defective pen + % chance of more than one defective pen = 100%
96% + % chance of exactly one defective pen + 3% = 100%
% chance of exactly one defective pen = 1%
