Step 1:
Let $X$ be the random variable denoting the number of alpha particles emitted in a 20 minutes interval .
$X$ follows a poisson distribution with mean =5 particles in a 20 minutes interval.
$\therefore \lambda=5$
$X\sim P(5)$
$P(X=x)=\large\frac{e^{-5}5^x}{x!}$$\quad x=0,1,2.........$
Step 2:
Probability of at least 2 emissions in a 20 minutes interval
$P(X\geq 2)=1-P(X<2)$
$\qquad\qquad=1-(P(X=0)+P(X=1))$
$\qquad\qquad=1-\big(\large\frac{e^{-5}5^0}{0!}+\frac{e^{-5}5^1}{1!}\big)$
$\qquad\qquad=1-0.0067(1+5)$
$\qquad\qquad=1-0.0067(6)$
$\qquad\qquad=1-0.0402$
$\qquad\qquad=0.9598$