I'm sorry to beat on this. I know it is beyond my grasp of the nuances of math but, when you give the dice example you have 3 different numbers that can possibly come up on the die to make a combination that equals 4. 1, 2 and 3. With the frogs you only have 2 possibilities, male or female, not 3. If the 2 represents the male frog, then 1 and 3 can't. If you were to say that #1 represents the male frog and #3 represents the female frog then the only combinations that you could roll to equal 4 would be a 1 and a 3 or a 3 and a 1. The #2 doesn't have any representation because the male and female are already represented by 1 and 3. In the frog situation you only have 2 different things (a male and a female) that you are trying to make 3 different combinations with. Why is it not true that, knowing that one of the 2 frogs is a male, there is only a 50% chance that the other one is a female. The whole situation is really only about 1 frog and whether or not it is a male or female. If you go and lick both frogs, you will 100% lick one male frog. The only unknown is what the 2nd frog will be, and there is an equal chance that it will be a male or female, (50% chance).