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) binomial distribution
B) Poisson distribution
C) hypergeometric distribution
D) None of the above.

Question

Quizplus · Accepted Answer

The situation fits the characteristics of a binomial distribution, where there are a fixed number of independent trials (30 questions), each trial has only two possible outcomes (right or wrong), the probability of success (getting a question right) is the same for each trial (1/4), and the trials are performed identically. The question asks for the probability of getting at least 20 questions right, which means the successful outcome is getting a question right and the number of trials (n) is 30. Therefore, we can use the binomial distribution to calculate the probability of getting at least 20 questions right.

A Multiple-Choice Test Has 30 Questions