Checkout service times are independent exponential with density e^(−x/10)/10,x≥0. On arrival one customer is already being served and has spent five minutes there. Find the probability your remaining queue time plus your own service exceeds 15 minutes.
Memorylessness makes the current customer’s remaining time exponential of mean 10, unaffected by the elapsed five minutes. Add your independent service of the same law: total is gamma with shape 2,rate 1/10. Survival at 15 is e^(−15/10)(1+15/10)=**(5/2)e^(−3/2), A**.
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