John may be the oldest, middle or youngest of his parents’
children. As such, there are seven possible ways in which sons and
daughters could have turned out in order of age: MFF, FMF, FFM, MMF, MFM,
FMM, MMM. Four of these include at least two males, so the probability
is 4 in 7.

On the other hand, we know that John’s oldest child is a
daughter. As such, there are only four permutations: FMM, FMF, FFM,
FFF. This gives a probability of 3 in 4 of another girl being
there.