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The waiter at an expensive restaurant has noticed that 60% [#permalink]

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03 Apr 2013, 18:06

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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?

Re: The waiter at an expensive resturant has noticed [#permalink]

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03 Apr 2013, 21:27

Tagger wrote:

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.

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:

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.

Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]

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17 Aug 2013, 22:25

Solving for X in the figure shown below we will get Couples for deserts as 75% And couples not ordering deserts =100-75=25%

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2set.JPG [ 14 KiB | Viewed 11645 times ]

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Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]

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18 Aug 2013, 16:31

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 %
_________________

Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]

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24 Jan 2014, 06:09

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%.
_________________

Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]

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13 Feb 2015, 00:24

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]

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13 Apr 2016, 05:44

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The waiter at an expensive restaurant has noticed that 60% [#permalink]

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08 Oct 2016, 12:50

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%

60% order (C+D) i.e Both = 60% of Total 20% of D is without C; i.e. 80% of D also orders C 80% of D = Both 80% of D = 60% of Total \(\frac{D}{Total} =\frac{60}{80} = \frac{3}{4}\) Hence, \(\frac{C}{Total} = \frac{1}{4}\) = 25%
_________________

If you analyze enough data, you can predict the future.....its calculating probability, nothing more!

Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]

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24 Dec 2016, 13:28

Bunuel wrote:

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

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.

what about (Neither) those who didnt order coffee nor desert

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:

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.

what about (Neither) those who didnt order coffee nor desert

To get the probability that the next couple will not order dessert we need the percentage of those who do not order dessert which is 25. Those 25% include Coffee/No Dessert and No Coffee/No Dessert (Neither).
_________________

Please help me to understand why is the equation is 60+0.2x = x. Why shouldn't it be solved as 60 + 20 = x.

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We are given that 20% of the couples who order dessert don't order coffee. We denoted those who order dessert by x, thus those who order dessert but don't order coffee is 20% of that, which is 0.2x.
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