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Para cada uma das 30 questões de uma prova objetiva são apresentadas 5 alternativas de respostas, das quais somente uma é correta. Considere as afi...

Para cada uma das 30 questões de uma prova objetiva são apresentadas 5 alternativas de respostas, das quais somente uma é correta. Considere as afirmacoes relativas à prova: I - Existem no máximo 150 maneiras diferentes de responder à prova. II - Respondendo aleatoriamente, a probabilidade de errar todas as questões é (0,8)¤¡. III - Respondendo aleatoriamente, a probabilidade de exatamente 8 questões estarem corretas é. Analisando as afirmações, concluímos que a) apenas III é verdadeira. b) apenas I e II são verdadeiras. c) apenas I e III são verdadeiras. d) apenas II e III são verdadeiras. e) I, II e III são verdadeiras.


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matematica_probabilidade_exercicios.pdf
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Estatística I Universidade Federal de PernambucoUniversidade Federal de Pernambuco

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I - Verdadeira. Como cada questão tem 5 alternativas, existem 5 possibilidades de escolha para a primeira questão, 5 para a segunda, e assim por diante. Portanto, o número total de maneiras diferentes de responder à prova é 5x5x5... (30 vezes) = 5^30, que é menor que 150. II - Falsa. A probabilidade de errar uma questão é de 4/5, e a probabilidade de errar todas as 30 questões é (4/5)^30, que é aproximadamente 0,00034. III - Falsa. A probabilidade de acertar uma questão é de 1/5, e a probabilidade de acertar exatamente 8 questões é (30 escolha 8) x (1/5)^8 x (4/5)^22, que é aproximadamente 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