The average time for the lotto draw to be seen in your television is 2.75 hrs. A. Find the probability you witness the show at least one from 10pm to 11pm? B. Find the probability you witness the show at least two from 11.30pm to 1.30am?
I am having difficulties answering the problem, I am confused should i have it 2.75/24 per day? also is there a sense that it takes just 1 hr for A and 14hrs in b?
They are saying that the average waiting time -- the time to get one instance -- is $2.75$ hours. So, in a given hour, you would expect to get $$ \lambda:=\frac{1}{2.75}=\frac{4}{11} $$ instances. Thus the number of sightings in an hour should be Poisson-distributed with parameter $\lambda$, and the number of sightings in $2$ hours should be Poisson-distributed with parameter $2\lambda=\frac{8}{11}$.
So, for (a): You are looking for the probability that a Poisson random variable with parameter $\frac{4}{11}$ is non-zero; this is $$ P(\text{Pois}(\tfrac{4}{11})>0)=1-P(\text{Pois}(\tfrac{4}{11})=0)=1-e^{-4/11}\approx0.305. $$
For (b), you have a Poisson random variable with parameter $\frac{8}{11}$ and you want $$ P(\text{Pois}(\tfrac{8}{11})\geq2)=1-P(\text{Pois}(\tfrac{8}{11})=0)-P(\text{Pois}(\tfrac{8}{11})=1)=1-e^{-8/11}-\frac{8}{11}e^{-8/11}\approx0.165. $$