Thread: A student takes a 5 question multiple choice quiz with 4 choices for each question.?

If the student guesses at random on each question, what is the probability that the student gets exactly 4 questions correct

35%
Probability of answering the first question correctly: 25%
probability of answering the second question correctly: 25%
probability of answering the third question correctly: 25%
probability of answering the fourth question correctly: 25%
probability of answering the fifth question incorrectly: 75%
add all that up and divide by how many questions you have.
175/5=35

and for those other answers, 3/1024 is NOT .29%

100%

1/4 x 1/4 x 1/4 x 1/4 x 3/4

First of all, you need to find out how many different arrangements or combinations of 4 correct answers exist. This is 5 C 4 = 5.
So the student can answer 4 correct questions in 5 different ways (each way corresponding to one of the 5 questions being answered wrong).
The student's chance of guessing the correct answer for any question is 25% (1 out of 4). The student's chance of guessing 4 correct answers is (0.25)^4 = 3.9 * 10 ^-3
Since these can occur in 5 different combinations, the required probability is 5* 3.9 * 10^-3 = 0.02 (roughly).
Hope that helped.