My wife鈥檚 parents have six children, the first three and the sixth of whom are girls. Four of these children have children of their own, seven in all, and all of them girls. I am aware that men in certain occupations are more likely to father girls but in this family the seven grandchildren have four different fathers. Is this purely coincidence, or are there other factors at work?
鈥� Without knowing all the details, I will venture that coincidence seems likely. Any fetus has approximately a 1-in-2 chance of being female; the chance of seven children all being girls is therefore 1 in 2 to the seventh power, or 1 in 128. These are not particularly long odds, and if you consider that one would probably find several other combinations remarkable too (all boys, for example, or exactly alternating girls and boys), the odds that any given set of six grandchildren will exhibit a 鈥渞emarkable鈥� pattern is low enough that such an occurrence is, in fact, unremarkable.
This question stems from the human ability to find patterns in random data. It has been observed that people鈥檚 expectation about what a random sequence looks like are actually quite different from a typical random sequence. With coin flips, for example, a person might cite 鈥淗THHTHTTHHHTTH鈥� as a typical sequence, but a truly typical random sequence might look more like 鈥淗HHHHTHHTTHHHH鈥�: less alternation, longer runs of one value, and a ratio of heads to tails that is often far from 0.5 for short sequences. This means, conversely, that sequences that actually are random often appear not to be random to most people.
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If the group eventually reached 15 grandchildren and all were girls, then I might raise an eyebrow and wonder whether there might be a non-random cause at work. But even here the probability is still low enough (1 in about 32,000) for it to have happened quite a few times by chance throughout history.
Ben Haller, Menlo Park, California, US