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Expected number of ratio of girls vs boys birth - Cross Validated 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 An unreasonable rule would be one in which the expected children per couple was infinite
probability - What is the expected number of children until having the . . . 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
How to resolve the ambiguity in the Boy or Girl paradox? 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)
Hypothesis testing: Fishers exact test and Binomial test 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
Understanding intuition of the Two child problem Inspired by this twitter thread, posting this question: I have two children, (at least) one of whom is a boy born on a Tuesday what is the probability that both children are boys? Via Joel Grus,
what is the difference between a two-sample t-test and a paired t-test When you use a paired T-test, you are essentially doing a one-sample test, where your one sample consists of the paired differences between outcomes in two groups If you create a new sample of these difference values and then apply the formula for a one-sample T-test, you will see that this is equivalent to the paired test