A newly discovered species has offspring that are always either female or male. Scientists have observed 9 births so far, 7 of which were female. We want to know the probability of a female on the next birth.

Our friend Ludwig suggests we reason as follows. We are going to observe 10 births total, so there were 2¹⁰ = 1024 possible sequences. Thus each sequence had the same prior probability: 1/1024.

According to Ludwig's way of reasoning, what is the probability the 10th birth will be female, given that 7 of the first 9 were?