[Statistical Physics] Probability of finding # photons in the mode

1. The problem statement, all variables and given/known data

A cavity contains black body radiation at temperature T = 500 K. Consider an optical mode in the cavity with frequency ω=2.5×10[itex]^{13}[/itex] Hz. Calculate

a) the probability of finding 0 photons in the mode
b) the probability of finding 1 photon in the mode
c) the mean number of photons in the mode.

2. Relevant equations

Possibly <n> = [itex]\frac{1}{exp(\frac{\hbar \omega}{k_{b} T})}[/itex]

3. The attempt at a solution

Plugging the numbers into the equation above gives the answer to c (I think), which comes out to 1.855. However I thought that you could only have 0 or 1 photons in a given mode.

Not sure how to go about a) and b).


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