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The maitre 'd at an expensive Manhattan restaurant has

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The maitre 'd at an expensive Manhattan restaurant has  [#permalink]

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New post Updated on: 27 Nov 2013, 04:45
7
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

58% (01:48) correct 42% (01:33) wrong based on 144 sessions

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The maitre 'd at an expensive Manhattan 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 maitre 'd seats will not order dessert?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-waiter-at-an-expensive-restaurant-has-noticed-that-150365.html

Originally posted by vshaunak@gmail.com on 03 Aug 2007, 02:58.
Last edited by Bunuel on 27 Nov 2013, 04:45, edited 1 time in total.
Added the OA.
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New post 03 Aug 2007, 12:10
Can one of you explain this in detail. I didnt understand the question
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New post 03 Aug 2007, 13:32
ywilfred wrote:
It's 20%. Draw a grid to find the answer.


could you use a venn diagram and just go with the number 100.


60 people order dessert and coffee... which is the union of D and C.

2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither.

B 25%
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New post 04 Aug 2007, 00:49
I read the question carefully again, should be 25%. Sorry for the mix-up. I solved it using a grid similarly. (Tried to attach the grid, but it wouldn't load)
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Re: PS Probability  [#permalink]

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New post 04 Aug 2007, 04:55
vshaunak@gmail.com wrote:
The maitre 'd at an expensive Manhattan 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 maitre 'd seats will not order dessert?
(A) 20%
(B) 25%
(C) 40%
(D) 60%
(E) 75%

80% of the couples who order dessert do order coffee, so if x% of the couples order dessert, 0.8x = 0.6 and x=75. As 75% of the couples order dessert, the probability that the next couple will not order dessert is 100-75= 25%
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New post 07 Aug 2007, 12:06
vshaunak@gmail.com wrote:
The maitre 'd at an expensive Manhattan 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 maitre 'd seats will not order dessert?
(A) 20%
(B) 25%
(C) 40%
(D) 60%
(E) 75%


We start with:

D - DnC - C
a - 60 - b

a + 60 + b = 100; or a + 4 = 40

The problem says: (a+60)/5 = a, then a=15 and b = 25, which is the solution. B.
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New post 07 Aug 2007, 13:14
B. 25%

Let's say the sample group is 100 for simplicity.

60 order dessert and coffee

but 20% who order dessert, don't order coffee. 1-.2 = .8

.8x = 60

x = 60/.8 (or if it's easier to visualize, multiply each side by 1.25)

this gives you x = 75

so 75% of couples order dessert, leaving 25% not ordering.
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New post 07 Aug 2007, 13:23
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vshaunak@gmail.com wrote:
The maitre 'd at an expensive Manhattan 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 maitre 'd seats will not order dessert?
(A) 20%
(B) 25%
(C) 40%
(D) 60%
(E) 75%


25%
Assume total = 100
d = total customer who order dessert
d-60 = (20/100)*d
d = 75
Therefore, total customer who order coffee only = 25, Probability = 25%.
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Re: The maitre 'd at an expensive Manhattan restaurant has  [#permalink]

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New post 27 Nov 2013, 04:35
1
As shown below.. Answer is 25
Attachments

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a.JPG [ 13.47 KiB | Viewed 2601 times ]


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Re: The maitre 'd at an expensive Manhattan restaurant has  [#permalink]

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New post 27 Nov 2013, 04:46
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The maitre 'd at an expensive Manhattan 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 maitre 'd 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:
Image
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-waiter-at-an-expensive-restaurant-has-noticed-that-150365.html
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New post 19 Aug 2018, 10:13
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