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Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #4320 Fun: (2.35) Difficulty: (2.21) Category: Probability Submitted By: mad-ade Corrected By: MarcM1098

Mad Ade has just inherited a hotel from his rich Auntie Climax.
The rooms are numbered from 101 to 550.
What is the probability that room number starts with 1, 2 or 3 and ends with 4, 5 or 6?

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 egeon Jun 18, 2002 There are only 299 rooms beginning with 1, 2 or 3; there is no room #100. supermew30 Jul 08, 2002 Does this hotel happen to serve kababs for dinner? JYMZY Jul 26, 2002 299/450 * 3/10 = 897/4500 = 299/1500. not quite 20% chance Poker Aug 01, 2004 Egeon: the fact that he miscounted the number of rooms that met the first criterion, while a mistake, does not effect the answer because the improperly listed room, #100, does not meet the second criterion and thus is not one of the 90 rooms that meets both. brainjuice Mar 31, 2006 i think your answer is wrong. it is not 300 rooms which are started with 1,2, or 3. It is 299! here the solution: 101-200 -> 200-101+1= 100 rooms 201-300 -> 300-201+1= 100 rooms 301-399 -> 399-301+1= 99 rooms so there are 100+100+99= 299 rooms not 300 rooms (you count room number 400) you answer still correct, because finding rooms which is started with 1,2,3 is no use.. MarcM1098 May 05, 2006 I changed 300 to 299 as others noticed above. leftclick Aug 02, 2007 Nice one ...although if I wanted to be picky, I'd say that hotel rooms aren't numbered linearly like that, usually the first number is the floor, and the other numbers are the room on that floor (in this case that would be rooms 101-150, 201-250, etc). But I don't want to be picky, so I won't say that Janus006 Apr 23, 2009 JYMZY: The first probability is indeed 299/450 (being assigned to a room that begins with 1, 2, or 3). However, your second probability -- 3/10 -- is incorrect. Let's break it down further. P(starting with 1) = 99/450 P(starting with 2) = P(starting with 3) = 100/450 The next probability changes, from what you list, however. P(ending with 4 or 5 or 6|started with 1) = 30/99 P(ending with 4 or 5 or 6|started with 2) = P(ending with 4 or 5 or 6|started with 3) = 30/100 Now, (99/450)*(30/99) = 1/15. Similarly, (100/450)*(30/100) = 1/15. And, 3*(1/15) = .2.