Hey, I don't know where to start with this question.

Question:

On a multiple-choice test of 10 questions, each question has 5 possible answers. A student is certain of the answers to 4 questions but is totally baffled by 6 questions. If the student randomly guesses the answers to those 6 questions, what is the probability that the student will get a score of 5 or more on the test? Express your answer correct to two decimal places.

Solution

Okay, so I am assuming that the 4 questions the student is certain about are guaranteed to be correct. That leaves the other 6. All I really need to find here is the probability of getting all 6 questions incorrect. So I believe that would be:

$\displaystyle (\frac{5}{4}) (\frac{5}{4}) (\frac{5}{4}) (\frac{5}{4}) (\frac{5}{4}) (\frac{5}{4}) $ which gives me: $\displaystyle \frac{4096}{15625} $.

So to find the probability that the student will get a score of 5 or more on the test is $\displaystyle 1 - \frac{4096}{15625} $ which gives an answer of: $\displaystyle 0.737856 $ (my calculator for some reason put it into decimal form -.-).

Did I do this question correctly? I actually originally had very little on this question at all, and as I was writing this out this solution came to me. Does this solution make sense?

- Thanks!