Customers enter Starbucks at a Poisson rate $\backslash$lambda

per hour. Starbucks is holding a sale: the final amount that i

th customer pays is max$($Yi$$Si$,0)$

$,$ where Yi

is the original amount that i

th customer pays and Si

is the arrival time $($in hour$)$ of i

th customer such that $0<=$S$1<=$S$2<=...$

$.$ Assume Yi$$i$.$i$.$d$.$Uniform$(2,4)$

for all i

$$s$.$ What is the probability that all customers that entered during the first hour spent less than $2$ in final amount?