Num teste tipo certo/errado, com 50 questões: a) Qual é a probabilidade de que o aluno acerte 80% das questões, supondo que ele as responda ao acas...

a) A probabilidade de que o aluno acerte 80% das questões, supondo que ele as responda ao acaso, é de 0,6104 ou aproximadamente 61,04%. Explicação: - X segue distribuição binomial com n=50 e p=0,5. - Acertar 80% das questões significa X = 40. - Utilizando a fórmula da distribuição binomial, temos: P(X = 40) = (50! / (40! * (50-40)!) ) * (0,5^40) * (0,5^(50-40)) P(X = 40) = 0,6104 ou aproximadamente 61,04%. b) Repetindo o problema, supondo que existam 5 alternativas de resposta para cada questão, a probabilidade de que o aluno acerte 80% das questões, supondo que ele as responda ao acaso, é muito menor do que no caso anterior. Para calcular essa probabilidade, precisamos ajustar o valor de p na fórmula da distribuição binomial, que passa a ser p = 0,2 (já que agora há 5 alternativas de resposta, e apenas uma delas é correta). Assim, temos: P(X = 40) = (50! / (40! * (50-40)!) ) * (0,2^40) * (0,8^(50-40)) P(X = 40) = 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