You examine each tree in a 25 ft by 25 ft section of forest and record whether or not that tree is infected. Based on historical data, the average number of trees that would be expected to be infected in a section of this size is $3$.
What is the probability that you would find at least $2$ infected trees in a section of this size?
(a) $0.7760$
(b) $0.8009$
(c) $0.2240$
(d) $0.5768$
My impression was that there is insufficient information. If the number of trees in the plot were given, I would compute $$\sum_{k=2}^N \binom Nk \bigg(\frac{3}N\bigg)^k \bigg(1-\frac{3}N\bigg)^{n-k}$$ but I don't have the denominator $N$. Is there a way to solve this?
HINT...This requires the use of the Poisson distribution with parameter $\lambda=3$, find $p(X\geq2)$