Word Problem

Question

A multiple-choice exam consists of 20 problems, each with five answer choices, exactly one of which is correct. What is the probability that you get at least half of the problems correct if you randomly guess on all problems?

Answer 1

In this case, we have 5 choices, only one of which is correct. So the probability of selecting the correct answer is 1/5 or 20%

 

Since a guess on one question is unrelated to a guess on subsequent questions, the overall probability remains at 20% for each question.

 

Thus, the probability of guessing correctly on 10 questions will be very small.

Answer 2

Did you study the binomial distribution yet? It gives info on the chance of getting exactly the number of problems right out of 20 for example. In your case, the percent chance of getting exactly 10 problems right in some specific order is (1/5)^10*(4/5)^10. Then multiply this by the possible orderings of getting the 10 - for example: Are the first 10 only right? or are only the odd ones right or only the even ones?? There are a total of 10 choose 20 combinations of these orderings. So the formula for getting exactly 10 right becomes (10 choose 20) * (1/5)^10*(4/5)^10. Then this is the percent chance of getting exactly 10 right for all possible orderings. Now do that formula for getting exactly 11, 12, 13 .. 20 right and sum them all up to get the probability of at least 10 right.