If I am given two fertilised eggs, what is the probability that they will hatch as a mixed pair?
(a) As a non-mathematician, I can see there are four permutations:
MM, FF, MF, FM and so the probability would be 1 in 2.
Or, (b) if one egg hatches as, say, a female, there is a 1 in 2 chance the other will be male.
(c) However another argument is that (before any eggs hatch) there are three possible combinations:
MM, FF, MF and so there is a 1 in 3 chance of a mixed pair.
Which is correct? Or is it that there is a 1 in 3 chance, but when one hatches, the probability changes to 1 in 2, much as for the Monty Hall problem?
Apologies if this is a nonsense question.
Thanks.
Best Answer
Answers a),b) are correct.
a) Assuming that each egg is assigned M/F independently, label the eggs 1 and 2. Then the probability of MM,FF,MF,FM is 1/4 each. Therefore the total probability of having one M and one F is 1/2.
b) This argument works as you can pick egg 1, wait for it to hatch and then you know there is 1/2 chance the second egg will differ.
The reasoning for c) is incorrect.
c) There are three possible combinations (if you don't label the eggs), but there are more ways for MF (/FM) to occur. It is not the case that every event is equally weighted.