Question

An instructor develops a four-option, multiple choice exam. A student decides to guess randomly on each question. Given that the probability of guessing correctly on each question is 0.25, answer the following questions:

a) Suppose the exam has 20 questions; What is the average grade you would expect the student to obtain by guessing?

b) Suppose there are only 5 questions, what is the probability of guessing 100% by guessing?

Answer 1

a) Since the probability to guess correctly on each question is .25, that means on average, a student who randomly guesses will get 25% of all of the questions correct. Since there are twenty questions, each question is worth five points. (100/20=5) Figure out 25 percent of 20 questions (20*.25=5) and then multiply by the amount of points per question. (5*5=25) So the average score will be 25.
b) The probability of getting a hundred by guessing can be determined by multiplying .25 five times, or .25^5. This is because the likelihood of getting the next question right by guess gets lower and lower, since the only way to get the next question right and still be on target would be to get the previous questions right as well. So .25*.25*.25*.25*.25= 0.0009765625 or .09%.
Hope that helps!