Question

Naruto is choosing between two venues that will deliver food to his house. With probability 1/3 he will choose Ramen Mania (R), and with probability 2/3 he will choose Sushi (S). If he chooses R, 15 minutes after making the call, the remaining time it takes the food to arrive is exponentially distributed with average 10 minutes. If he orders S, 10 minutes after making the call, the time it takes the food to arrive is exponentially distributed with an average of 12 minutes. Given that he has already waited 25 minutes after calling, and the food has not arrived, what is the probability that he ordered from R?

I am really stuck on how to set this up, so if you could be extra clear, that would be super helpful! Thanks in advance

Answer 1

1/% Naruto Choohes R witw putaatiry 19 n LAR henen, 15 mimh aften makng aun Lan Sis chene 10 Imins fter maang n Can 12 mi ns 11 We ragnire nlrenty trai'ted 25 mins -4ter Caking R. he has he trdered from Frrd has mt-mivad P Raiting tome fism R naird 25 mi PC PCwaired frder ter fom R) P( CheingR minh der from R) P(cherting R) P(raird a5 25nitrden fom ) P (Aring P( 15+x >ス5| x~Exp (mlan>10 Expm an2-1 25 P P( t4+y5Exr men 12)) P(x >101X-EM(10). P(x> 101 NEP(10)) P(Y151E(12)

waired 7 25 mnnd frmR) P 15.x 7-25 1 Km FUr (49) 7. trden fam p(Armt725mins 7 P (1 y72lyEar (14) ). 10 プァ10 Ex(a) where X + yz 15 hang 1 24