A multiple choice examination has $10$ questions, each of which has $4$ possible answers.Suppose that for each question a student knows the correct answer with probability $0.8$ and guesses with probability $0.2$. Find the probability that the student will correctly answer exactly $9$ questions?
My solution:
P(Exactly 9 correct answers)= $10$ * $(0.8)^9$ * $0.2$
The given solution answer is $0.3474$.
How should I solve this?
Best Answer
Basic approach. The student knows the correct answer with probability $0.8$ and guesses with probability $0.2$—presumably, they guess each of the four possible answers with equal likelihood. Therefore, the probability that they submit the correct answer is greater than $0.8$. How much more is it? Use that value instead of $0.8$ in the binomial expansion, and you should obtain the right answer.