Question

An exam consists of 10 true-or-false questions. If a student guesses at every answer, what is the probability that he or she will answer exactly 6 questions correctly? (Round your answer to three decimal places.)

Answer 1

This can be solved by using the binomial distribution. The probability of guessing correctly is 0.5, and the probability of making a wrong guess is also 0.5.
$P(6\ correct)=10C6\times(\frac{1}{2})^{6}\times(\frac{1}{2})^{4}=\frac{210}{1024}=0.205$