You are taking a 10 question
multiple choice test. If each question has four choices and
you guess on each question, what is the probability of getting
exactly 7 questions correct?
n = 10
k = 7
n – k = 3
p = 0.25 = probability of guessing the correct
answer on a question
q = 0.75 = probability of guessing the
wrong answer on a question
P(7 correct guesses in 10 questions) = \(\left( {\begin{array}{*{20}{c}}{10}\\7\end{array}} \right){\left( {0.25} \right)^7}{\left( {0.75} \right)^3} \approx 0.0031\)
