Question 12
Suppose that there are $n$ students standing in a line, and each student randomly raises either their left or right hand, but not both. Let $P_n$ denote the probability that in every group of three students standing in a row, at least one student raised their right hand. Prove
$$
P_n \lt \left(\frac{12}{13}\right)^{n-2}.
$$
$$
P_n \lt \left(\frac{12}{13}\right)^{n-2}.
$$