Fraternal Twins

[Jokodo]

Megeth,

re: "Three outcomes with equal probability..."


Actually, there are four possible outcomes.

Not the way you stated the problem, there's not. Consider the "truth table":

GB
BG
GG
BB

Now, that looks like four, but is only three, as GB/BG are the same as order is ignored/not specified in the problem, and are thus considered as one possible outcome (one is a girl).

So only three possible and equally probable outcomes...one is a girl, both are girls, or neither is a girl, and the probability that one is a girl is one in three.

I think I disagree.

The problem specifically mentions fraternal twins - which is when two separate eggs are fertilized by two separate sperm. Thus there are two separate chances for a girl. No different than flipping two coins simultaneously (order still doesn't matter). The probability of exactly one girl is .5 and the probability of at least 1 girl is .75.

(Or to say it differently, there are only 3 outcomes, but they are not all equally likely)

aa

If you flip two coins simultaneously, there are three possible and equally likely outcomes if order is not considered - one is heads, both are heads, or neither are heads.

The only way to get the .5/.75 result/truth table is if you specify order is significant.

I will gladly play poker with anyone who disagrees.

You'll loose.

If if order is not considered, then there are three possible outcomes, but they're not equally likely. The coin doesn't know whether order is going to be considered when it falls. So the probability of 1 heads, 1 tails in the order is not considered scenario has to be exactly the same as the probability of heads-tails + the probability of tails-heads when it is considered. That makes 2/4.