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Numa pesquisa sobre preferência de detergentes realizada numa população de
100 pessoas, constatou-se que 62 consomem o procuto , 47 cansoment
produto e 10 pessoas não consomem nem e nem que parte desta
populacaão consome tanto o produto quanto o produto ?

Ask by Carroll Kirk. in Brazil
Mar 30,2025

Solución de inteligencia artificial de Upstudy

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Responder

19 pessoas consomem tanto o produto quanto o produto .

Solución

Seja o número de pessoas que consome ambos os produtos e . Como 10 pessoas não consomem nenhum produto, o número de pessoas que consome pelo menos um dos produtos é:
Pela fórmula da união de dois conjuntos, temos:
Substituindo os valores:
Simplificando, obtemos:
Resolvendo para :
Portanto, 19 pessoas consomem tanto o produto quanto o produto .

Respondido por UpStudy AI y revisado por un tutor profesional

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Mind Expander

Para resolver essa questão, podemos usar o princípio da inclusão-exclusão.
  1. Temos 100 pessoas no total, e 10 não consomem nem nem . Portanto, 90 pessoas consomem pelo menos um dos produtos.
  2. Se 62 consomem e 47 consomem , a soma é .
  3. Como temos 90 pessoas consumindo pelo menos um dos produtos, o número de pessoas que consomem tanto quanto é dado pela soma dos consumidores menos o total de consumidores:
    Onde representa as pessoas que consomem ambos.
    Assim, substituindo os valores:
Portanto, 19 pessoas consomem tanto o produto quanto o produto .

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