# Stumped on how to answer multi step probability question.

• Mar 3rd 2010, 11:59 AM
Kakariki
Stumped on how to answer multi step probability 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!
• Mar 3rd 2010, 01:00 PM