Basic probability : the frog riddle - what are the chances? 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 ?

It depends on the probability of croaking. If we assume that there are an equal number of croaking males (C) and silent males (S), then we can draw the sample space (females being F):
CS
SC
CF
CF
FC
FC
Where CF and FC are repeated twice as there are twice as many females than croaking males or silent males. Thus, assuming the probability of a frog croaking is 1/2, the probability of there being a female is 2/3.
