User:Pk2912/sandbox

Example
Let us consider a multiple choice question test that contains 10 questions, each question has 4 choices.

You need to get 6 questions right to pass!

$p_i(correct)=1/4 , p_i(incorrect)=3/4 $

No. of ways to select k questions = $$n!/(k!(n-k)!) = \tbinom{n}{k}$$

$$P(X=k) = \tbinom{10}{k}*(1/4)^k (3/4)^{10-k}$$

The chances of getting 6 questions right and passing the test are :

$$P(X\geq6) =P(X= 6) + ... +P(X= 10) = 0.0197$$