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A couple decides to keep having children until they have the same number of boys and girls, and then stop. Assume they never have twins, that the "trials" are independent with probability 1/2 of a boy, and that they are fertile enough to keep producing children indefinitely. Expected girls from one couple$ {}=0.5\cdot1 + 0.25\cdot1 =0.75$ Expected boys from one couple$ {}=0.25\cdot1 + 0.25\cdot2 =0.75$ 1 As I said this works for any reasonable rule that could exist in the real world.
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An unreasonable rule would be one in which the expected children per couple was infinite. Expected number of ratio of girls vs boys birth - Cross Validated Probability of having 2 girls and probability of having at least one girl Ask Question Asked 8 years, 7 months ago Modified 8 years, 7 months ago Probability of having 2 girls and probability of having at least one girl 1st 2nd boy girl boy seen boy boy boy seen girl boy The net effect is that even if I don't know which one is definitely a boy, the other child can only be a girl or a boy and that is always and only a 1/2 probability (ignoring any biological weighting that girls may represent 51% of births or whatever the reality is). Considering the population of girls with tastes disorders, I do a binomial test with number of success k = 7, number of trials n = 8, and probability of success p = 0.5, to test my null hypothesis H0 = "my cake tastes good for no more than 50% of the population of girls with taste disorders". In python I can run binomtest(7, 8, 0.5, alternative="greater") which gives the following result ...
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3 "Given that boys' heights are distributed normally $\mathcal {N} (68$ inches, $4.5$ inches$)$ and girls are distributed $\mathcal {N} (62$ inches, $3.2$ inches$)$, what is the probability that a girl chosen at random is taller than a boy chosen at random?"