HL CHAPTER 8 Are You Smarter Than Google?

CHAPTER 8 Are You Smarter Than Google?
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each couple keeps having children until they have a boy, then they stop. What fraction of the population is female?
Note:IL QUESTITO CHE HA FATTO INFIAMARE IL PUBBLICO

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the question is meant to be answered in expectation,

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NULLA È CERTO QUI

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Google has used it to screen job candidates.
Note:UN QUESITO CON UNA STORIA

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simple, clear, and wrong.
Note:LA RISPOSTA UFFICIALE

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Each birth has a 50 percent chance of producing a girl.
Note:RISPOSTA UFFICIALE...

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half of all the children are girls.
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it does not follow—and in fact is not true!—that in expectation, half of all children are girls.
Note:PURTROPPO DALLE PREMESSE CORRETTE

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the number of boys and the number of girls are equal.
Note:QUEL XHE SEGUE...CHE NN È LA STESSA COSA

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2 Eggs and Pancakes
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two eggs and one pancake.
Note:A COLAZIONE SE ESCE TESTA

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two eggs and three pancakes.
Note:SE ESCE CROCE

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every day) I have exactly two eggs.
Note:UNA COSA È CERTA

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two pancakes
Note:MEDIAMENTE

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the number of pancakes is equal to the number of eggs.
Note:MEDIAMENTE....

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Whenever I flip heads, ⅓ of my breakfast items are pancakes. Whenever I flip tails, ⅗ of my breakfast items are pancakes. The average of those two numbers is 7/15.
Note:LA RISPOSTA ESAYTA

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equal in expectation,* but that tells you nothing about their expected ratio.
Note:REGOLA GENERALE CON DUE ELEMENTI

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the correct answer depends on the size of the country.
Note:PRIMA CONSIDERAZIONE

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one family.
Note:1/2 MASCHIO 1/4 UN MASCHIO UNA FEMMINA 1/8 UN MACHIO DUE FEMMINE

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multiply it by the corresponding probability,
Note:NUMERO MEDIO DI BAMBINE ATTESE....QUELLO DEI MASCHI È UNO...ANXHE PER LE BAMBINE È UNO

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the expected number of girls is equal to the expected number of boys—just
Note:PRENDIAMO UNA FAMIGLIA MEDIA

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But to get the expected fraction of girls, we need to do the same calculation with fractions of girls
Note:MEDIA FRAZIONI...30%

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that calculation is only correct for a country with just one family.
Note:RICORDIAMOCI

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For a country with two families, a similar but more complicated calculation gives an expected fraction of about 38.63 percent.
Note:DUE FAMIGLIE

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For a country comparable to the United States, with about 100 million families, the expected fraction is about 49.999999975 percent.
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