Question

A true-false examination has 48 questions. June has probability 3/4 of answering a question correctly. April just guesses on each question. A passing score is 30 or more correct answers. Compare the probability that June passes the exam with the probability that April passes it.

Christian’s Response:

We can calculate the probability of both June and April passing the exam using binomial distribution. The pnorm function can be used to perform this calculation.

Below we’re going to calculate June’s chances of passing the exam:

june <- 3/4
n <- 48
prob_june <- pbinom(30-1, n, june, lower.tail = FALSE)
cat("The probability that june passes the exam is", prob_june)
## The probability that june passes the exam is 0.9816458

Below we’re going to calculate April’s chances of passing the exam:

april <- 1/2
prob_april <- pbinom(30-1, n, april, lower.tail = FALSE)
cat("The probability that april passes the exam is", prob_april)
## The probability that april passes the exam is 0.05570145

Though I expected June’s chances to be higher, I didn’t expect the difference between June and April to be so far apart.