A multiple-choice test has 30 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all questions randomly. What type of probability distribution can be used to figure out his chance of getting at least 20 questions right?
A) hypergeometric distribution
B) binomial distribution
C) Poisson distribution
D) none of the above

Question

Quizplus · Accepted Answer

The binomial distribution can be used in this scenario because it models the probability of a certain number of successes in a given number of trials, where each trial has a fixed probability of success. In this case, the student either gets a question right or wrong (success or failure), and the probability of success (getting a question right) is constant at 1/4 for each trial (each question). Therefore, the binomial distribution is appropriate for calculating the probability of the student getting at least 20 questions right out of 30.

A Multiple-Choice Test Has 30 Questions