Question: 2014 Fall Midterm - 17
Assume you write a multiple-choice exam that consists of 100 questions. For each question, 4 options are given, one of which is the correct one. If you answer each of the 100 questions by choosing an answer uniformly at random, what is the probability that you have exactly one correct answer?
a) $\frac{100}{4^{100}}$
b) $\frac{3^{99}}{4^{100}}$
c) $\frac{100 + 3^{99}}{4^{100}}$
d) $\frac{100 \cdot 3^{99}}{4^{100}}$
Assume you write a multiple-choice exam that consists of 100 questions. For each question, 4 options
are given, one of which is the correct one. If you answer each of the 100 questions by choosing an
answer uniformly at random, what is the probability that you have exactly one correct answer?
(a)
$\frac{100 + 3^{99}}{4^{100}}$
(b)
$\frac{100 \cdot 3^{99}}{4^{100}}$
(c)
$\frac{3^{99}}{4^{100}}$
(d)
$\frac{100}{4^{100}}$