Buses arrive at a specified stop at 15 minute intervals starting at 7 A M That is, they arrive at 7, 7 15, 7 30, 7 45, and so on If a passenger arrives at the stop at a time that is uniformly distributed between 7 and 7 30, find the probability that he waits (a) less than 5 minutes for a bus (b) at least 12 minutes for a bus x 0 30 3,2 a less than 5 min for a bus 7 10 7 25 , P(10 x 15) P(25 A communications system consists of n components, each of which will, independently, function with probability p The total system will be able to operate effectively if at least one half of its components function (a) For what values of p is a 5 component system more likely to operate effectively than a 3 component system 5 component 5 1 5 2 5 needs at least 3 components working ( 5 ) (P) (1 P) p5 ( ) (P) (1 P) 5p (1 P) ( ) (P) (1 p) 10 p (1 P) e 3 Component 3 1 5 2 needs at least 2 components working ( 3 ) (P) (1 p) p 13 (3) (P) (1 p)' 3p (1 p) 10p (1 p) 5 (1 p) p 3 (1 2) p factor p 10p (1 P) 5p (1 p) p 3 (I p) 3 6p 15 p 10p 2p 3 6p3 15p 3 p 12p 0370 2p 5 p 4p 170 P 1, PLI Ans P Input 2p 5p 4p 1 0 Inequality plot 0 06 0 04 0 02 0 4 0 6 0 8 1 0 1 2 0 02 0 04 Alternate forms (p 1) (p ) 0 (p 1) (2p 1) 0 Solutions p 1 1

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Question: Buses arrive at a specified stop at 15-minute intervals starting at 7 A.M. That is, they arrive at 7, 7:15, 7:30, 7:45, and so

Buses arrive at a specified stop at 15-minute intervals starting at 7 A.M. That is, they arrive at 7, 7:15, 7:30, 7:45, and so on. If a passenger arrives at the stop at a time that

Buses arrive at a specified stop at 15-minute intervals starting at 7 A.M. That is, they arrive at 7, 7:15, 7:30, 7:45, and so on. If a passenger arrives at the stop at a time that is uniformly distributed between 7 and 7:30, find the probability that he waits (a) less than 5 minutes for a bus; (b) at least 12 minutes for a bus. x = [0 30] = [3,2] a. less than 5 min for a bus 7:10 7:25 , P(10 < x

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