Hotel Ade
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
Mad Ade has just inherited a hotel from his rich Auntie Climax.
The rooms are numbered from 101 to 550.
A room is chosen at random for Mad Ade's first guest.
What is the probability that room number starts with 1, 2 or 3 and ends with 4, 5 or 6?
Answer
There are total 450 rooms.
Out of which 299 room numbers start with either 1, 2 or 3.
Now out of those 299 rooms only 90 room numbers end with 4, 5 or 6.
So the probability is 90/450 i.e. 1/5 or 0.20
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Comments
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:
101200 > 200101+1= 100 rooms
201300 > 300201+1= 100 rooms
301399 > 399301+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 101150, 201250, 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 6started with 1) = 30/99
P(ending with 4 or 5 or 6started with 2) = P(ending with 4 or 5 or 6started with 3) = 30/100
Now, (99/450)*(30/99) = 1/15. Similarly, (100/450)*(30/100) = 1/15. And, 3*(1/15) = .2. 
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