An R Introduction to Statistics

Binomial Distribution

The binomial distribution is a discrete probability distribution. It describes the outcome of n independent trials in an experiment. Each trial is assumed to have only two outcome, labeled as success or failure. If the probability of a successful trial is p, then the probability of having x successful trials in an experiment is as follows.

( ) n x (n−x) f(x) = x p (1 − p) where x = 0,1,2,...,n

Problem

Suppose there are twelve multiple choice questions in an English class quiz. Each question has five possible answers, and only one of them is correct. Find the probability of having four or less correct answers if a student attempts to answer every question at random.

Solution

Since only one out of five possible answers is correct, the probability of answering a question correctly by random is 1/5=0.2. To find the probability of having four or less correct answers by random attempt, we apply the function pbinom with x = 4, n = 12, p = 0.2.

> pbinom(4, size=12, prob=0.2) 
[1] 0.92744

Answer

The probability of four or less questions answered correctly by random in a twelve question multiple choice quiz is 92.7%.

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