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The waiter at an expensive restaurant has noticed that 60%

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The waiter at an expensive restaurant has noticed that 60% [#permalink] New post 03 Apr 2013, 17:06
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The waiter at an expensive restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability that the next couple the waiter seats will not order dessert?

A. 20%
B. 25%
C. 40%
D. 60%
E. 75%
[Reveal] Spoiler: OA

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Last edited by Bunuel on 04 Apr 2013, 02:28, edited 1 time in total.
Renamed the topic and edited the question.
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Re: The waiter at an expensive resturant has noticed [#permalink] New post 03 Apr 2013, 20:27
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The waiter at an expensive resturant has noticed that 60% of the couples order desert and coffee. However, 20% of the couples who order desert dont order coffee. what is the probability that the next couple the waiter seats will not order desert?

A.) 20%
B.) 25%
C.) 40%
D.) 60%
E.) 75%


Let the number of people ordering only desert = d, only ordering coffee be c and ordering both be b. Given that , 20 % of (b+d) = d

or 4d = b.

Thus, as b = 60, d = 15. The total number of people not ordering desert = 100-(60+15) = 25.

B.
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Re: The waiter at an expensive restaurant has noticed that 60% [#permalink] New post 04 Apr 2013, 02:46
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Expert's post
Tagger wrote:
The waiter at an expensive restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability that the next couple the waiter seats will not order dessert?

A. 20%
B. 25%
C. 40%
D. 60%
E. 75%


Probably the best way to solve this question is using the double set matrix, as shown below:
Attachment:
Coffee and Dessert.png
Coffee and Dessert.png [ 3.79 KiB | Viewed 5487 times ]
From above, we have that 60+0.2x=x --> x=75.

Thus, the probability that the next couple will not order dessert (yellow box) is 100-75=25.

Answer: B.

Hope it's clear.
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Re: The waiter at an expensive restaurant has noticed that 60% [#permalink] New post 17 Aug 2013, 21:25
Solving for X in the figure shown below we will get Couples for deserts as 75%
And couples not ordering deserts =100-75=25%
Attachments

2set.JPG
2set.JPG [ 14 KiB | Viewed 4440 times ]


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Re: The waiter at an expensive restaurant has noticed that 60% [#permalink] New post 18 Aug 2013, 15:31
Tagger wrote:
The waiter at an expensive restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability that the next couple the waiter seats will not order dessert?

A. 20%
B. 25%
C. 40%
D. 60%
E. 75%



Let, total dessert ordered = T and total couple = 100
From question,
60+20% of T = T
or, T = 75 % ordered dessert.

So next couple will not order dessert = 100-75 = 25 %
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Re: The waiter at an expensive restaurant has noticed that 60% [#permalink] New post 24 Jan 2014, 05:09
Let total number of couples be 100.

60% order Dessert & Coffee = 60 couples.
20% who order Dessert do not order coffee => 80% who order dessert also order coffee this is given to be 60.
Hence total number of couples who order Dessert is 60*100/80 = 75.
Number of couples who do NOT order Dessert = 100-75 = 25.
The probability that next order will not have dessert is 25%.
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Re: The waiter at an expensive restaurant has noticed that 60% [#permalink] New post 12 Feb 2015, 23:24
Tagger wrote:
The waiter at an expensive restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability that the next couple the waiter seats will not order dessert?

A. 20%
B. 25%
C. 40%
D. 60%
E. 75%


I solved this pretty fast this way:

60% dessert and coffee
--> 40% nothing, dessert, or coffee

Let them be the same probability --> 40% / 3 = 13,333%

40% - 13% = 27% --> Answer has to be around this range --> B is closest
Re: The waiter at an expensive restaurant has noticed that 60%   [#permalink] 12 Feb 2015, 23:24
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