Subscribe to Blog via Email
December 2020 S M T W T F S « Jan 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Sometimes people never learn. Jacque Wilson, in a piece for CNN titled: Calculating the odds: 12 sons in a row reports the odds at about 1 in 4000.
The problem first is in calculating the odds after discovering an instance of the event. I can’t just flip a coin 12 times, get 12 heads and say the odds of that are one in 4000. Any sequence of flips – heads and tails – is just as likely to happen. We only focus on twelve heads because it appears unique to us. Look at 4000 such sequences and one sequence of 12 heads is likely to happen. The actual odds are (1-0.5*(*12))**4000 of not having an incidence of 12 heads in the 4000 tries. 1-0.5**12 is the odds of it not happening in a single trial. That is very high at 0.9998. but after 4000 trials the odds of not seeing it happen is about 0.37.
With the situation with the twelve sons, the second exponent is not 4000, but the number of women with 12 children.
But it does not stop there as the story could have been written had the reported discovered any woman with a large number of children of the same sex. If the subject of this story come to her attention when she had ten sons she could have written a similar story. With all the possible ways the story could have been generated it is impossible to calculate the exact probability.
And the reporter commits an even graver error. She goes on to note that child number 13 is due in May and then goes on to say the odds of having a 13th son is 1 in 8000. I’m sorry the odds are very close to 1 in 2. The other 12 have already arrived – they have no real influence on the odds of 13th child being a boy or a girl.