22. In 1710, J. Arbuthnot observed that male births had exceeded female births in London for 82 successive years. Arguing that the two sexes are equally likely, and 2-82 is very small, he attributed this run of masculinity to Divine Providence. Let us assume that each birth results in a girl with probability p = 0.485, and that the outcomes of different confinements are independent of each other. Ignoring the possibility of twins (and so on), show that the probability that girls outnumber boys in 2n live births is no greater than (2) p"q"{q/(q − p)}, where q = 1 - p. Suppose that 20,000 children are born in each of 82 successive years. Show that the probability that boys outnumber girls every year is at least 0.99. You may need Stirling's formula.

22. In 1710, J. Arbuthnot observed that male births had exceeded female births in London for 82 successive years. Arguing that the two sexes are equally likely, and 2-82 is very small, he attributed this run of masculinity to Divine Providence. Let us assume that each birth results in a girl with probability p = 0.485, and that the outcomes of different confinements are independent of each other. Ignoring the possibility of twins (and so on), show that the probability that girls outnumber boys in 2n live births is no greater than (2) p"q"{q/(q − p)}, where q = 1 - p. Suppose that 20,000 children are born in each of 82 successive years. Show that the probability that boys outnumber girls every year is at least 0.99. You may need Stirling's formula.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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