An estimated 2011 world Birth Rate was about 4 births per second
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Assuming that the chance of a woman giving birth to a boy or a girl is the same (in reality there's about 105 boys born for every 100 girls) then the probability of 22 of the same gender births *in a row* is: P=(0.5)^22=0.0000002384 or 1 in 4,194,304 It depends on the "when" of the question. If you point at a childless woman, and say "She will give birth to 22 children. What is the likelyhood that they will all be girls?" In that case the probability will be one in two-to-the-twenty-second. Pretty long odds. BUT, if you point at a woman with twenty one children, and ask "What are the odds that the next one will be a girl?" Then the answer is one in two. Make sense?
Assuming that the births at the hospital are equally likely to be of either gender then the answer is (1/2)4 = 1/16
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Births and Deaths
Ans : Probability that there will be at least one case of twins = 1-(79/80)^20