I'm looking for a third opinion on the probability of making a particular decision due to chance alone.
I have a task where people read a paragraph of text, then they are shown it a second time, except some of those times one word has changed. People are then asked whether they detected a change. If they say no then that's the end of the task. If they say yes, then they are given a set of nine words and are asked to respond which word was changed.
If people correctly guess that a change has occurred AND which word was changed, then a single "correct" is registered. If they correctly detect a change and wrongly guess the word that has changed then an "incorrect" is registered (similarly, it is incorrect if a word has changed but the person did not detect it).
What I'm trying to work out is what is the probability of correctly answering that a word has change, AND which word it was, due to chance alone. My first thought was that it was 1/18. That's a 1/2 chance of firstly correctly guessing that a change had occurred, followed by a 1/9 chance of correctly guessing the word.
Someone I've spoken to has suggested that the chance rate is actually 1/10. In effect, "no, a change has not occurred" becomes the tenth option.
So, is the chance of being correct 1/18, 1/10, or are we both wrong?