Binomial Probability Formula:

P(k successes in n trials) = \(\left( {\begin{array}{*{20}{c}}n\\k\end{array}} \right){p^k}{q^{n - k}}\)

n = number of trials
k = number of successes
n – k = number of failures
p = probability of success in one trial
q = 1 – p = probability of failure in one trial

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) = \(\left( {\begin{array}{*{20}{c}}{10}\\7\end{array}} \right){\left( {0.25} \right)^7}{\left( {0.75} \right)^3} \approx 0.0031\)