in the movies

can someone help me!!!!! i've been stuck in this problem for hours now!!! ack!!!! heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp meeeeeeeeeeeeeeeeeeeeeeee pleeeeeeeeeeeeeeeeeeease!!!!!

the manager of a movie theater determines that the average time moviegoers wait in line to buy a ticket for this week's film is 10 minutes and the average time they wait to buy popcorn is 5 minutes. assuming that the waiting times are independent, find the probability that a moviegoer waits a total of less than 20 minutes before taking his or her seat.
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just underneath that question there is a caveat that i hadn't noticed before. it gives a hint to something my statistics book does not cover.

"Hint: assume that both the waiting time X for the ticket purchase and the waiting time Y in the refreshment line are modeled by the exponential probability density functions."

i did a google on such functios but it all looks very complicated. i'm just confused why my statistics book would throw something at me that it doesn't even explain. :(
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alright... it took me AAAAAAAAAAAAAAAAALLLLLLLL night but i finally got it figured out thanks to wikipedia!!!!

i got an answer of 76% so it better be right!!!!


TS Contributor
Sounds like a reasonable answer, but I'll have to dust off my Operations Research notes from grad school to double-check it.:D