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wu :: forums    riddles    medium (Moderators: Grimbal, Icarus, Eigenray, SMQ, ThudnBlunder, william wu, towr)    Bus stop « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Bus stop  (Read 707 times) Altamira_64 Junior Member     Posts: 116 Bus stop   « on: Jul 3rd, 2012, 1:58pm » Quote Modify A public bus arrives at the bus stop sometime between 6:00 and 6:30. A passenger arrives at the same bus stop some random time within this time interval. What is the probability that the passenger catches the bus within 5 minutes from the time he arrives at the stop? IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Bus stop   « Reply #1 on: Jul 3rd, 2012, 10:23pm » Quote Modify I get 11/36, by drawing a diagram IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Altamira_64 Junior Member     Posts: 116 Re: Bus stop   « Reply #2 on: Jul 4th, 2012, 1:05am » Quote Modify Well, I get 11/72, which one is correct?? IP Logged rmsgrey Uberpuzzler     Gender: Posts: 2873 Re: Bus stop   « Reply #3 on: Jul 4th, 2012, 3:30am » Quote Modify I get 11/72, assuming that the passenger can't catch the bus when the bus arrives first; 11/36 if the bus waits 5 minutes at the stop. IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Bus stop   « Reply #4 on: Jul 4th, 2012, 8:43am » Quote Modify I thought it was a bit high... I had (30*30/2-25*25/2)/900, and somehow ended up with 275/900 (or in other words, I neglected to divide 900-625=275 by 2) IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Altamira_64 Junior Member     Posts: 116 Re: Bus stop   « Reply #5 on: Jul 4th, 2012, 9:49am » Quote Modify I assume that the bus can't wait for the passenger, if it arrives first. It has to go.   So I guess that for the first 25 minutes (25/30 of the total time) the probability is stable, 25/30, that is, 1/6. For the last 5 mins (5/30 of the total time), it decreases linearly and eventually gets to zero.   In effect, the total probability is: 25/30 * 1/6 + 5/30 * 1/6 * 1/2 = 11/72. IP Logged rmsgrey Uberpuzzler     Gender: Posts: 2873 Re: Bus stop   « Reply #6 on: Jul 6th, 2012, 5:10am » Quote Modify I solved it with a diagram - plot bus arrival time against passenger arrival time, and you get a strip between tB=tP and tB=tP+5, the area of which is 1/2 - (1/2)(5/6)(5/6) (the triangle from the main diagonal less the triangle from the other diagonal line) or 11/72 IP Logged lopez Newbie     Posts: 10 Re: Bus stop   « Reply #7 on: Jul 12th, 2012, 3:05am » Quote Modify I get 11/72 IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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