Answer in Statistics and Probability for Michael #119400

Let “n=10” (number of questions) and “p=1/5” (the probability to choose correct answer).

Now we can consider “X” – number if correct answers, and “Xsim Bin(10,1/5)”

We need to find “P(Xgeq 6)” – the probability that he will get at least six questions correct.

For “Xsim Bin(n,p)” we have: “P(X=k)=binom n k p^k (1-p)^{n-k}”

“P(Xgeq 6)=P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)=210 times(1/5)^6 (4/5)^4+120times (1/5)^7(4/5)^3+45times (1/5)^8(4/5)^2+10times (1/5)^94/5+1times(1/5)^{10}approx 0.0064”

Answer: 0.0064