A male friend of yours wants to test if you are ok at Math and logical thinking, he says I am one of two children of my parents, and asks you to find out the probability that his sibling is a sister, he carefully also states he wants you to assume a sex ratio of 100 boys to 100 girls and that they were not twins.
The accepted answer has a subtle error. If we randomly select a 2-sibling family with at least one male, the odds of the other being female are indeed 2/3. If we randomly select a male who is part of a 2 person family, the odds of them having a male sibling are 1/2.
The three, equally probable male-containing families are
MF FM MM
There are four males listed, and 2 of them have male siblings.
(Edit to remove irrelevant female only family)
Edit again: Note that if you were to randomly select 2-child families with at least one male instead, (for example, by selecting a group of fathers and asking for those with 2 children and at least 1 male) you'd get 2/3 of them having a girl
The fact that the first child among two is a boy has no effect on the sex of the second because the draw "sex of the first child" and "sex of the second child" are independant.
The probability of the other sibling being a girl is equal to the probability for any child picked at random to be a girl.
The chance is 1/2.
Another form of the question would be:
You play heads or tails -with a balanced coin, no loophole- twice.
The first time you play you get heads, what is the chance for the second time you play for it to get tails ?
It is 1/2. The chance for you to get tails is not increased by the fact that you had heads previously.
As soon as we know that the first child is a male, FM and FF become impossible, leaving MF and MM.
EDIT: I see that I still am not the accepted answer. And after discussing with my friend I can see why.
My answer is counter intuitive because in real life people tend to apply the Law of Large Numbers -or law of averages- to their everyday / low amount of draws routines. For instance:
You are at the casino, and play roulette.
You place your bets on red and lose 3 times.
You apply the law of average and believe that now your chance to win by betting red is very high. But this reasoning is irrational. The roulette has no memory of the previous rolls. Your chances by betting red or black are still the same.
Let me make another attempt at making you see that Skywalker's answer is flawed.
A group of 4 male dudes come to you at a party and tell you that they have a 5th friend of which they ask you to guess the gender.
According to the logic used in his argument the chance for the 5th friend to be a girl is 4/5 = 0.80 = 80% because the possible combinations are
MMMMM MMMMF MMMFM MMFMM MFMMM FMMMM
The fact that the 4 other dudes are males bring no knowledge of the gender of the 5th.
The chance in that case is 1/2 too.
it doesn't state in the question that ether of the offspring are male or female, it says a male friend of yours asks you(the reader) a question... etc. the variables you are speaking of(as far as the existing sex of the alive child, not the child to come into play in the question) will change depending on the sex of the reader, also still does not change the outcome of the end result, for the odds reset for each child born, even if the children born are all male so far, it does not mean that there is a higher or lower likelihood of the next being male or female, it is still a 50/50 shot, mathematically... while scientifically speaking if the father is predisposed to produce one sex more than the other then there would be a 2/3 likelihood that the child in question would be born male or female.