Question 5
A gambling student tosses a fair coin and scores one point for each head that turns up and two points for each tail. Prove that the probability of the student scoring exactly $n$ points is
$$
\frac{1}{3}\left[2+\left(-\frac{1}{2}\right)^{n}\right].
$$
$$
\frac{1}{3}\left[2+\left(-\frac{1}{2}\right)^{n}\right].
$$