Answer to Question #119595 in Statistics and Probability for Benard

Question

Emmanuel is given a multiple-choice exam with ten questions and each question with
five possible answers. He decided to guess randomly for each question. What is the
probability that he will get at least six questions correct?

Answer 1

According to the binomial distribution formula the probability of answering exactly X questions is:

$P(X)=C^X_{10}\cdot(\frac{1}{5})^X\cdot(\frac{4}{5})^{10-X}$

Then:

$P(X\geq6)=P(6)+P(7)+P(8)+P(9)+P(10)\\ \approx 0.0064$