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	Probabilistically speaking, what is the expected number of children a couple should have in order to get both a boy AND a girl? Combien d’enfants un couple devrait avoir pour faire en sorte d’obtenir, avec un taux de probabilité élevé, une fille et un garcon? Quanti pargoli dovrebbe avere una coppia per far sì di ottenere, con un alto grado di probabilità, una femmina e un maschio? You can comment and discuss this puzzle on our FaceBook or Blogger web page. › Click to show/hide the solution Solution: Three… The parents first have children of both genders after the birth of nth child, provided the first n – 1 children are of the same gender and the nth child is of the opposite gender. This can happen in 2 ways out of a possible 2n. The probability is thus 1/2n-1 or 21-n. In reality, this is a rather inaccurate model, since it ignores (amongst other factors) the fact that the ratio of boys to girls is not exactly 50:50, and the possibility of identical twins (who are always the same gender). However, this problem is about probability and not biology. So the expected number of children is: Sum[n · 21-n] = 3 (assuming that initial n = 2) Please spread the word about the Sunday Puzzle!

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Text and images by Gianni A. Sarcone 
Labels: SUNDAY PUZZLE, puzzles to solve, recreational mathematics, probability
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