Question

A multiple choice exam is made up of 10 questions; Each question has 5 options and only one of them is correct. If a person answers at random, what is the probability of answering only 3 good questions?

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Hermann

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Fórmula de probabilidad binomial P(X=k)=(n,k)*p^k * (1-p)^(nk)
n=10 (10 preguntas)
k=3 (3 respuestas correctas)
p=1/5 (probabilidad de responder correctamente a una pregunta, ya que hay 5 opciones y solo una es correcta
P(X=3)=(10,3)*(1/5)^3 * (4/5)^7
P(X=3)= (10!/3!7!)(1/5)^3 * (4/5)^7 = 0,201
Entonces, la probabilidad de responder correctamente sólo 3 preguntas es aproximadamente 0,201, o 20,1%.

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