jonnythan:You're reading way to much into it. 50% say they work, not 50% say they ONLY work.
Besides, if they were independent, you'd have 110%, so they can't possibly be independent. It's much simpler than you seem to think
Well, I didn't want to infer the absence or presence of the "only", on general principles.
Indeed, however, I didn't even bother to look at the numbers to see if the percentages given might indicate which choices are pertinent (D'oh!).
Old reflex, make the student think clearly in formulating the question before proceeding. Half the time, that heads straight for the answer immediately with no further discussion.
Ultimately, my goal was to show the path without walking it hand-in-hand.
Two cardinal rules of probability & statistics:
1. The question is way more important than the answer, and extreme clarity there is crucial.
2. From that point onwards, ultimately it is just simple, careful counting (as you demonstrate).
Cheers,
Walter