What are the odds of identifying a man in a photo?

Question

I have a feeling the answer is going to go completely over my head, but I'm asking anyway. I have a photograph taken in 1939 of a boat. I know a fair amount about the crew and circumstance at the moment the photograph was taken. Let's assume 20 souls aboard (might have been 19; still working on that). All men. I know the names of 11 of the souls and I have additional photographs of all 11. The primary subject of my research is one of the 11: his name is Lawrence. At the moment this photograph was taken, all 20 were aboard, including Lawrence. In the photo, 3 men are visible on deck but it's a bit out of focus. All else being equal, is it fair to say that the odds of Lawrence being one of those three men is 3 in 20? Supposing I were to positively identify one of the three and take him out of the equation. Does that change the odds to two in 19? Now suppose I could say the captain (another one of the 11) is absolutely NOT one of the two remaining unidentified men on deck. How does that change the bottom line to answer the question, "What are the odds that Lawrence is one of the men in this photograph?"

Answer 1

Hi John A.,

Yes to first thought, 3/20.

Yes to 2nd thought, 2/19.

What do you know new in the third situation? Simply that the captain must be below decks; thus, your sample space is now only 18 souls. Your probability of Lawrence is now 2/18. Assuming that you know that Lawrence is not the captain! If he is, P=0. !! Also, we assume that there are not 2 crew named each Lawrence. ("I'm Lawrence of the Gulf of Arabia"....)

You should perhaps take note that there are probability puzzles that have unexpected interactions with known/unknown data, the Monty Hall problem is the famous one. You might want to look it up, and analyse thoroughly why you should change your door choice in that situation.

-- Cheers, --Mr. d.