The correct answer is a) 0.1934.
The binomial distribution is
[tex](_k^n)p^k(1-p)^{n-k}[/tex], where n is the number of trials (questions), k is the number of successes (correct answers), and p is the probability of a success (0.5 on true-false questions). Using our information we have:
[tex](_5^{12})(0.5)^5(1-0.5)^{12-5}
\\
\\=(_5^{12})(0.5)^5(0.5)^7
\\
\\=\frac{12!}{5!7!}(0.5)^5(0.5)^7
\\
\\=792(0.5)^5(0.5)^7
\\=0.1934[/tex]
