A few days ago I was watching this video The frog riddle and I have been thinking a lot about this riddle.
In this riddle you are poisoned and need to lick a female frog to survive. There are 2 frogs behind you and basically, you have to find what are your chances to find a least one female in these two frogs (you can lick both of them). The only thing is : you know one of them is a male (because your heard the croak) but you don't know witch one.
The video solves the problem with conditional probability and explains that you have a 2/3 chance of getting a female. (on the four possibilities MM / MF / FM / FF, knowing there is a male eliminates FF)
Here is my question : If you see which one is a male (for example the frog on the left is a male) what are your chances to survive ? Is it 1/2 ? because we only have two possibilities (MM or MF) with probability 1/2. Is it still 2/3 because the position does not matter ?
Bonus question : If it is 1/2, then if close your eyes and the frogs can move, is it still 1/2 or does it comes back to 2/3 ?
Similar problem : If I have two children, and I know one is a son, then I have a 67% chance to have a daughter. But if I know the oldest one is a son, then I have a 50% chance to have a daughter. Is it exactly the same problem here ?
Can you please explain this to me ?