An unprepared student must take a 7-question, multiple-choice test that has 5 possible answers per question. If the student can eliminate 2 of the possible answers on the first 4 questions, and if she guesses on every question, what is the probability that she will answer every question correctly?
A)Pr(all correct) =
B)Pr(all correct) =
C)Pr(all correct) =
D)Pr(all correct) =
E)Pr(all correct) =

Question

An unprepared student must take a 7-question, multiple-choice test that has 5 possible answers per question. If the student can eliminate 2 of the possible answers on the first 4 questions, and if she guesses on every question, what is the probability that she will answer every question correctly? ​
A)Pr(all correct) = 
B)Pr(all correct) = 
C)Pr(all correct) = 
D)Pr(all correct) = 
E)Pr(all correct) =

Quizplus · Accepted Answer

Since the student can eliminate 2 out of 5 possible answers on the first 4 questions, she now has a 1 in 3 chance of guessing correctly on each of those questions. For the remaining 3 questions, she has a 1 in 5 chance of guessing correctly. Therefore, the probability of answering all 7 questions correctly would be (1/3)^4 * (1/5)^3, which simplifies to approximately 0.0000803. This matches Option B.

An Unprepared Student Must Take a 7-Question, Multiple-Choice Test That