Question

William is taking the 25-question, multiple choice American Mathematics Competition. Each question has five answer choices. William guesses random answers for the last four questions. What is the probability that he will get at least one of these final four questions right?

Answer 1

Given that William guesses random answers for the last four questions and that each question has five answer choices.

The probability that he gets an answer correct is 1 / 5.

The probability that he did not get an answer correct is 4 / 5.

The probability that he will not get any of the 4 questions correctly is

$\left( \frac{4}{5} \right)^4= \frac{256}{625}$

Therefore, the probability that he gets at least one of the 4 questions correctly is

$1-\frac{256}{625}= \frac{369}{625} =0.59=59\%$