Poisson Distribution #stat

Question

I posted early a bit a same question but I wanted to know if I'am doing alright another one. Let $X$ be the number of customers buying a book in a bookstore e-shop. Assume $X$ has a Poisson distribution with a mean of 1 books bought every 10 minutes.

1. (a) What is the probability that no one will buy a book in the next hour?
2. (b) What is the probability that there is at least one book bought in the next minute?

My solution

a) $P(x=0) = e^{-6}$

b) $P(X\ge 1)=1-e^{-1/10}$

Answer 1

$\lambda$ = 1,

Thus $\lambda t = 6$ books/hour

Part I $P(X = 0 ) = \dfrac{e^{-6}.6^0}{0!}$

Part II Thus $\lambda t = 0.1 $books/minute

$P(X>1) = 1-P(X=0)$

$P(X=\text{0 in a minute}) = \dfrac{e^{-0.1}.0.1^0}{0!}$