The probability of finding a particle in a state with energy $E$ is
$\begin{align*}\frac{e^{-E/kT}}{\sum_i e^{-E_i/kT}}\end{align*}$
where the summation is over all states $i$ . If there are only two states, and we would like probability that the particle is found in state $i=2$ , then this equation gives
$\begin{align*}\boxed{\frac{e^{-E_2/kT}}{e^{-E_1/kT} + e^{-E_2/kT}}}\end{align*}$
Therefore, answer (B) is correct.

Solution to 2008 Problem 78