I try to solve the following exercise:
A multiple choice exam has n questions. Each question has $3$ answers of which only one can be valid. The student requires $60\%$ correct answer to pass the exam. How many questions are needed so that the student has a probability of $(\le 0.1\%)$ to pass the exam while guessing the answers.
I am stuck with this exercise. With $X$ for passing the exam $$X \sim B(p=\frac{1}{3},n=?)$$
$P(X \geq ?) \leq 0.001$ but am not sure how to go with that.
HINT - You need to solve the following inequality:
$$\sum\limits_{k=\lceil0.6n\rceil}^{n}\binom{n}{k}\cdot\left(\frac13\right)^{k}\cdot\left(1-\frac13\right)^{n-k}<0.001$$