The flowers appear according to a Poisson process with rate 3 per hour.
Given that 8 flowers appeared between 9 a.m. and 10 a.m., what is the probability that 3 of them appeared between 9 a.m. and 9:20 a.m.?
The answer given is $${8 \choose 3} \frac{1}{3}^3 \frac{2}{3}^5$$ I understand ${8 \choose 3}$ because we need to know the probability of 3 of the 8 flowers appearing. Also, we are looking a third of the hour. Hence, ${\frac{1}{3}^3}$.
But where does $\frac{2}{3}^5$ come into play? I assume it the probability that the other 5 flowers do not appear.
Lastly, is there a way to formulate a correct answer using a Poisson process?
Thanks!