Answer
The probability that an excited atom will emit a photon is $~~0.02$
Work Step by Step
Let $P$ be the probability that an excited atom will emit a photon.
We can find $P$:
$P = \lambda~\Delta t$
$P = (\frac{1}{\tau})~(\Delta t)$
$P = \frac{\Delta t}{\tau}$
$P = \frac{0.50~ns}{25~ns}$
$P = 0.02$
The probability that an excited atom will emit a photon is $~~0.02$
