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.
We can model each of these as a binomial distribution with June having \(p=0.75\) and April having \(p=0.5\). Thus:
1-pbinom(29,48,.75)## [1] 0.9816458June’s chance of passing the exam is approximately 98.2% and…
1-pbinom(29,48,.5)## [1] 0.05570145April’s chance of passing the exam is approximately 5.6%.