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# In a hotel with single rooms and double rooms, what is the probability

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Math Expert
Joined: 02 Sep 2009
Posts: 52296
In a hotel with single rooms and double rooms, what is the probability  [#permalink]

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28 Jan 2018, 22:42
00:00

Difficulty:

45% (medium)

Question Stats:

51% (01:07) correct 49% (01:05) wrong based on 71 sessions

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In a hotel with single rooms and double rooms, what is the probability that a room chosen at random will be a double room painted red?

(1) 1/6 of the rooms in the hotel are painted red.
(2) 2/3 of the hotel's rooms are double rooms.

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Re: In a hotel with single rooms and double rooms, what is the probability  [#permalink]

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28 Jan 2018, 23:04
Has to be E.

Clearly statement 1 and 2 are insufficient.

Combination case:

Lets say there are 18 rooms and lets put this is table format.

In first case the probability=1/3
Attachment:
File comment: Case 1

!.JPG [ 18.25 KiB | Viewed 485 times ]

In second case the probability=2/3
Attachment:
File comment: Case 2

2.JPG [ 17.99 KiB | Viewed 485 times ]

Hence insufficient.
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Re: In a hotel with single rooms and double rooms, what is the probability  [#permalink]

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28 Jan 2018, 23:04
Bunuel wrote:
In a hotel with single rooms and double rooms, what is the probability that a room chosen at random will be a double room painted red?

(1) 1/6 of the rooms in the hotel are painted red.
(2) 2/3 of the hotel's rooms are double rooms.

Probability that a room will be double room and painted red = (Number of double rooms which are painted red) / (total number of rooms)
We need this ratio. Let the number of total rooms = X.

(1) X/6 are red painted, but we dont know about double rooms. Not Sufficient.

(2) 2X/3 are double rooms, but we dont know about rooms which are painted red. Not Sufficient.

Combining the two statements, we still dont know the fraction of rooms which are double as well as painted red. Eg, if we assume X=6, then 1 room is red and 4 rooms are double rooms (as per data in the two statements). But we dont know whether that 1 red room is a double room or a single room.

So Not sufficient. Hence E answer
Re: In a hotel with single rooms and double rooms, what is the probability &nbs [#permalink] 28 Jan 2018, 23:04
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