Question:
A student takes a multiple choice test with 20 questions. Each question has 5 possible answers, only one of which is correct.
a)If a student knows the answer to each question with probability 0.9 , what is the chance they will answer at least 14 correctly?
I am not sure how to go about this.
What I have tried:
P(correct) = p(known) + p(unknown) x p(chosencorrect)
P(correct)= 0.9+ 0.1 x 0.2
P(correct) = 23/25
P(14) = 20C14 x (23/25)^14 (4/5)^6 (Option 1)
P(14) = 20C14 x (23/25)^14 (0.5/5)^6 (Option 2)
P(14) = 20C14 x (0.9/(23/25))^14 (4/5)^6 (Option 3 - employing conditional probability)
First time working with this, hence the errors.
Would someone please tell me where I am going wrong?