A quiz consists of 10 multiple choice questions each with fi

A quiz consists of 10 multiple choice questions, each with five possible answers, one of which is correct. To pass the quiz a student must get 60% or better on the quiz. If a student randomly guesses, what is the probability that the student will pass the quiz?

How do I do this?

Solution

the student will pass the quiz if he has at least 6 questions correct

Given X follows Binomial distribution with n=10 and p=1/5=0.2

P(X=x)=10Cx*(0.2^x)*(0.8^(10-x)) for x=0,1,2,...,10

So the probability is

P(X>=6) = P(X=6)+P(X=7)+...+P(X=10)

=10C6*(0.2^6)*(0.8^(10-6))+....+10C10*(0.2^10)*(0.8^(10-10))

=0.006369382