Question

Emmanuel is given a multiple choice exam with ten questions and each question with 5 possible answers.He decided to guess randomly for each question. What is the probability that he will get at least 6 questions correct

Answer 1

There are 10 questions, n=10

Probability of getting a correct answer in one question is $\frac {1}{5}$ =0.2

This is a binomial distribution case

$P(X=x) ={n \choose x } p^x q^{n-x}$

$P(X\ge 6)=\sum_{i=6}^{10}{10\choose x} 0.2^x 0.8^{10-x}$

=0.006369