Samuel Pharma takes care of product distribution by trucks loaded at its only loading station. Samuel$$s trucks and their $3$rd party logistic provider $($Amba Logistics$)$ are used for this purpose. It was observed that on an average every $5$ minutes, one truck arrived and the average loading time was $3$ minutes. $50\%$ of the trucks belong to Amba Logistics. Find the following:

a$)$ Probability that a truck has to wait.

b$)$ The waiting time of truck that waits

c$)$ The expected waiting time of contractor$$s truck per day $($before being loaded$)$ assuming a $24-$ hour shift